library(tidyverse)
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr     1.1.4     ✔ readr     2.1.5
## ✔ forcats   1.0.0     ✔ stringr   1.5.1
## ✔ ggplot2   3.5.1     ✔ tibble    3.2.1
## ✔ lubridate 1.9.3     ✔ tidyr     1.3.1
## ✔ purrr     1.0.2     
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
library(gtsummary)
library(emulator)
## Loading required package: mvtnorm
test_df=read_csv('Project_1_data.csv') %>% janitor::clean_names() 
## Rows: 948 Columns: 14
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (10): Gender, EthnicGroup, ParentEduc, LunchType, TestPrep, ParentMarita...
## dbl  (4): NrSiblings, MathScore, ReadingScore, WritingScore
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
test_df=test_df %>%  
  mutate(is_first_child=case_when(
    is.na(is_first_child) &nr_siblings==0 ~ 'yes',
    TRUE ~is_first_child
  )) %>% 
        mutate(gender=as.factor(gender),
               ethnic_group=as.factor(ethnic_group),
               parent_educ=as.factor(parent_educ),
               lunch_type=as.factor(lunch_type),
               test_prep=as.factor(test_prep),
               parent_marital_status=as.factor(parent_marital_status),
               practice_sport=as.factor(practice_sport),
               is_first_child=as.factor(is_first_child),
               transport_means=as.factor(transport_means),
               wkly_study_hours=as.factor(wkly_study_hours)) %>% drop_na()
summary(test_df)
##     gender     ethnic_group             parent_educ         lunch_type 
##  female:315   group A: 50   associate's degree:129   free/reduced:207  
##  male  :275   group B:123   bachelor's degree : 71   standard    :383  
##               group C:175   high school       :123                     
##               group D:156   master's degree   : 39                     
##               group E: 86   some college      :116                     
##                             some high school  :112                     
##      test_prep   parent_marital_status   practice_sport is_first_child
##  completed:210   divorced: 93          never    : 69    no :192       
##  none     :380   married :344          regularly:219    yes:398       
##                  single  :138          sometimes:302                  
##                  widowed : 15                                         
##                                                                       
##                                                                       
##   nr_siblings      transport_means wkly_study_hours   math_score    
##  Min.   :0.000   private   :229    < 5   :156       Min.   :  0.00  
##  1st Qu.:1.000   school_bus:361    > 10  :104       1st Qu.: 56.25  
##  Median :2.000                     10-May:330       Median : 67.00  
##  Mean   :2.129                                      Mean   : 66.74  
##  3rd Qu.:3.000                                      3rd Qu.: 78.00  
##  Max.   :7.000                                      Max.   :100.00  
##  reading_score    writing_score   
##  Min.   : 17.00   Min.   : 10.00  
##  1st Qu.: 60.00   1st Qu.: 58.00  
##  Median : 70.00   Median : 69.00  
##  Mean   : 69.87   Mean   : 68.92  
##  3rd Qu.: 81.00   3rd Qu.: 79.00  
##  Max.   :100.00   Max.   :100.00
test_df %>% 
  ggplot(aes(x=math_score))+geom_histogram()
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

test_df %>% 
  ggplot(aes(x=reading_score))+geom_histogram()
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

test_df %>% 
  ggplot(aes(x=writing_score))+geom_histogram()
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

stu_data=table(test_df$gender,test_df$ethnic_group)

chisq.test(stu_data)
## 
##  Pearson's Chi-squared test
## 
## data:  stu_data
## X-squared = 7.211, df = 4, p-value = 0.1251
# Loop through pairs of columns and run the chi-square test

for (i in 1:(11 - 1)) {
  for (j in (i + 1):11) {
    # Get the two columns to test
    col1 <- test_df[[i]]
    col2 <- test_df[[j]]
    
    contingency_table <- table(col1, col2)
    
    # Perform the chi-square test
    chi_test <- chisq.test(contingency_table)
    
    #PRint the results 
    if(chi_test$p.value<.05){
      
      
      cat("Chi-square test for columns", colnames(test_df)[i], "and", colnames(test_df)[j], "\n")
    print(chi_test)
    

    }
    
  }
}
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Chi-square test for columns gender and nr_siblings 
## 
##  Pearson's Chi-squared test
## 
## data:  contingency_table
## X-squared = 15.086, df = 7, p-value = 0.03491
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Chi-square test for columns is_first_child and nr_siblings 
## 
##  Pearson's Chi-squared test
## 
## data:  contingency_table
## X-squared = 45.266, df = 7, p-value = 1.214e-07
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
ggplot(test_df, aes(x = nr_siblings, fill = gender)) +
      geom_bar(position = "fill") +
      labs(y = "Proportion", title = "Pairwise Relationship")

ggplot(test_df, aes(x = nr_siblings, fill = is_first_child)) +
      geom_bar(position = "fill") +
      labs(y = "Proportion", title = "Pairwise Relationship")

Writing Score

df_4_mdl_write=test_df %>% dplyr::select(gender,ethnic_group,parent_educ,lunch_type,test_prep,parent_marital_status,practice_sport,is_first_child,transport_means,wkly_study_hours,writing_score)
full_fit_write=lm(writing_score ~ .^2,data=df_4_mdl_write)
summary(full_fit_write)
## 
## Call:
## lm(formula = writing_score ~ .^2, data = df_4_mdl_write)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -36.097  -6.757   0.000   7.512  25.909 
## 
## Coefficients: (4 not defined because of singularities)
##                                                           Estimate Std. Error
## (Intercept)                                                77.5056    16.5568
## gendermale                                                -11.5459     8.4352
## ethnic_groupgroup B                                       -14.6713    14.2358
## ethnic_groupgroup C                                       -23.6506    13.4300
## ethnic_groupgroup D                                        -6.5467    14.6194
## ethnic_groupgroup E                                        -0.6452    13.7011
## parent_educbachelor's degree                               32.2994    14.9679
## parent_educhigh school                                      8.9108    12.3906
## parent_educmaster's degree                                -13.3428    20.4548
## parent_educsome college                                    -9.2192    12.1578
## parent_educsome high school                                 0.3856    11.7932
## lunch_typestandard                                          3.1104     8.3745
## test_prepnone                                             -18.8143     8.7378
## parent_marital_statusmarried                               16.0430    11.1254
## parent_marital_statussingle                                10.7223    13.3899
## parent_marital_statuswidowed                               43.4838    39.5573
## practice_sportregularly                                   -23.0508    13.3196
## practice_sportsometimes                                   -19.7741    13.2523
## is_first_childyes                                          14.2090     9.5945
## transport_meansschool_bus                                  -3.2352     8.4932
## wkly_study_hours> 10                                      -19.5441    13.0836
## wkly_study_hours10-May                                      1.6614    10.5143
## gendermale:ethnic_groupgroup B                              4.3932     5.3431
## gendermale:ethnic_groupgroup C                              9.3149     5.1384
## gendermale:ethnic_groupgroup D                              5.8109     5.1043
## gendermale:ethnic_groupgroup E                              5.3001     5.6595
## gendermale:parent_educbachelor's degree                    -3.1793     4.4945
## gendermale:parent_educhigh school                           1.0620     3.6653
## gendermale:parent_educmaster's degree                       9.9155     6.2928
## gendermale:parent_educsome college                         -4.1300     3.8491
## gendermale:parent_educsome high school                      0.2529     3.7808
## gendermale:lunch_typestandard                              -1.2039     2.6255
## gendermale:test_prepnone                                   -0.2240     2.6166
## gendermale:parent_marital_statusmarried                    -0.4821     3.7301
## gendermale:parent_marital_statussingle                     -0.1518     4.2288
## gendermale:parent_marital_statuswidowed                     1.2933    18.3113
## gendermale:practice_sportregularly                         -3.0622     4.4464
## gendermale:practice_sportsometimes                         -3.2602     4.4697
## gendermale:is_first_childyes                                3.0435     2.7466
## gendermale:transport_meansschool_bus                       -0.1546     2.5389
## gendermale:wkly_study_hours> 10                            -3.8677     3.9831
## gendermale:wkly_study_hours10-May                          -2.6013     3.0208
## ethnic_groupgroup B:parent_educbachelor's degree           -8.3345    12.4645
## ethnic_groupgroup C:parent_educbachelor's degree           -8.4712    12.4445
## ethnic_groupgroup D:parent_educbachelor's degree           -9.6856    12.3505
## ethnic_groupgroup E:parent_educbachelor's degree          -16.9547    14.0557
## ethnic_groupgroup B:parent_educhigh school                -16.1825     7.8036
## ethnic_groupgroup C:parent_educhigh school                -10.7952     7.5005
## ethnic_groupgroup D:parent_educhigh school                 -7.6467     7.6256
## ethnic_groupgroup E:parent_educhigh school                -11.4328     8.4924
## ethnic_groupgroup B:parent_educmaster's degree              4.9001    14.9754
## ethnic_groupgroup C:parent_educmaster's degree             -7.4679    13.9097
## ethnic_groupgroup D:parent_educmaster's degree              2.9024    14.1310
## ethnic_groupgroup E:parent_educmaster's degree              1.3629    14.8684
## ethnic_groupgroup B:parent_educsome college                 3.2143     8.6301
## ethnic_groupgroup C:parent_educsome college                 5.9797     8.1460
## ethnic_groupgroup D:parent_educsome college                 9.5674     8.4844
## ethnic_groupgroup E:parent_educsome college                 2.6023     8.5774
## ethnic_groupgroup B:parent_educsome high school           -17.7650     8.2716
## ethnic_groupgroup C:parent_educsome high school           -10.3880     7.7610
## ethnic_groupgroup D:parent_educsome high school            -6.6709     7.8120
## ethnic_groupgroup E:parent_educsome high school            -4.3383     8.3877
## ethnic_groupgroup B:lunch_typestandard                      3.1284     5.5561
## ethnic_groupgroup C:lunch_typestandard                      6.9223     5.3886
## ethnic_groupgroup D:lunch_typestandard                      3.8322     5.3042
## ethnic_groupgroup E:lunch_typestandard                     -0.1953     6.1469
## ethnic_groupgroup B:test_prepnone                           2.4242     5.6685
## ethnic_groupgroup C:test_prepnone                           6.4991     5.3175
## ethnic_groupgroup D:test_prepnone                           4.2882     5.3281
## ethnic_groupgroup E:test_prepnone                          10.4184     5.7998
## ethnic_groupgroup B:parent_marital_statusmarried            4.0514     7.6528
## ethnic_groupgroup C:parent_marital_statusmarried           -0.2301     7.0469
## ethnic_groupgroup D:parent_marital_statusmarried          -10.9053     6.9504
## ethnic_groupgroup E:parent_marital_statusmarried           -4.3960     7.6897
## ethnic_groupgroup B:parent_marital_statussingle            10.5415     9.0607
## ethnic_groupgroup C:parent_marital_statussingle             2.1275     8.5665
## ethnic_groupgroup D:parent_marital_statussingle            -2.6676     8.2778
## ethnic_groupgroup E:parent_marital_statussingle             3.1117     9.5410
## ethnic_groupgroup B:parent_marital_statuswidowed           73.8433   101.3778
## ethnic_groupgroup C:parent_marital_statuswidowed          114.3340    82.3923
## ethnic_groupgroup D:parent_marital_statuswidowed           12.1039    83.0580
## ethnic_groupgroup E:parent_marital_statuswidowed                NA         NA
## ethnic_groupgroup B:practice_sportregularly                14.5020    10.1514
## ethnic_groupgroup C:practice_sportregularly                15.9609    10.0599
## ethnic_groupgroup D:practice_sportregularly                11.8248    11.2295
## ethnic_groupgroup E:practice_sportregularly                12.9574    10.2802
## ethnic_groupgroup B:practice_sportsometimes                12.6309    10.8289
## ethnic_groupgroup C:practice_sportsometimes                22.0758    10.5328
## ethnic_groupgroup D:practice_sportsometimes                12.1147    11.6115
## ethnic_groupgroup E:practice_sportsometimes                12.5339    10.5863
## ethnic_groupgroup B:is_first_childyes                       9.7409     5.6253
## ethnic_groupgroup C:is_first_childyes                       3.4474     5.3065
## ethnic_groupgroup D:is_first_childyes                       1.8617     5.3681
## ethnic_groupgroup E:is_first_childyes                       2.7052     6.0462
## ethnic_groupgroup B:transport_meansschool_bus              -7.4751     5.6284
## ethnic_groupgroup C:transport_meansschool_bus             -11.2746     5.1972
## ethnic_groupgroup D:transport_meansschool_bus              -5.1875     5.1920
## ethnic_groupgroup E:transport_meansschool_bus             -12.0724     6.1289
## ethnic_groupgroup B:wkly_study_hours> 10                   -5.9602     9.5818
## ethnic_groupgroup C:wkly_study_hours> 10                    1.9360     9.4624
## ethnic_groupgroup D:wkly_study_hours> 10                    6.7581     9.4492
## ethnic_groupgroup E:wkly_study_hours> 10                    0.4986    10.2937
## ethnic_groupgroup B:wkly_study_hours10-May                 -5.8066     8.0474
## ethnic_groupgroup C:wkly_study_hours10-May                  1.8457     7.8744
## ethnic_groupgroup D:wkly_study_hours10-May                  2.9555     8.0075
## ethnic_groupgroup E:wkly_study_hours10-May                 -1.4251     8.6215
## parent_educbachelor's degree:lunch_typestandard             0.9925     4.8362
## parent_educhigh school:lunch_typestandard                   0.9740     3.9027
## parent_educmaster's degree:lunch_typestandard               6.9772     7.1530
## parent_educsome college:lunch_typestandard                  5.3543     3.9343
## parent_educsome high school:lunch_typestandard              5.7895     4.0754
## parent_educbachelor's degree:test_prepnone                 -1.3131     4.4623
## parent_educhigh school:test_prepnone                        1.8447     4.2737
## parent_educmaster's degree:test_prepnone                   -2.3089     7.6077
## parent_educsome college:test_prepnone                      -1.8819     4.0056
## parent_educsome high school:test_prepnone                   2.4708     3.8740
## parent_educbachelor's degree:parent_marital_statusmarried -17.2754     7.9642
## parent_educhigh school:parent_marital_statusmarried         2.5731     5.6012
## parent_educmaster's degree:parent_marital_statusmarried     4.5317     8.1036
## parent_educsome college:parent_marital_statusmarried       -4.8368     5.5157
## parent_educsome high school:parent_marital_statusmarried   -3.8229     5.4356
## parent_educbachelor's degree:parent_marital_statussingle  -16.6290     8.5852
## parent_educhigh school:parent_marital_statussingle          6.4988     6.1186
## parent_educmaster's degree:parent_marital_statussingle      1.5045     8.6504
## parent_educsome college:parent_marital_statussingle        -4.6580     6.1430
## parent_educsome high school:parent_marital_statussingle    -3.7573     6.0684
## parent_educbachelor's degree:parent_marital_statuswidowed -20.6113    84.4043
## parent_educhigh school:parent_marital_statuswidowed       -74.8517    92.8678
## parent_educmaster's degree:parent_marital_statuswidowed   -98.2733    48.6482
## parent_educsome college:parent_marital_statuswidowed      -87.5058    60.9959
## parent_educsome high school:parent_marital_statuswidowed  -61.8441    73.1065
## parent_educbachelor's degree:practice_sportregularly        1.8608     8.2226
## parent_educhigh school:practice_sportregularly            -10.9775     7.0762
## parent_educmaster's degree:practice_sportregularly          1.5289     9.9993
## parent_educsome college:practice_sportregularly            -0.1518     7.1960
## parent_educsome high school:practice_sportregularly        -3.2753     6.9492
## parent_educbachelor's degree:practice_sportsometimes       -8.3616     7.8902
## parent_educhigh school:practice_sportsometimes            -10.1532     6.7020
## parent_educmaster's degree:practice_sportsometimes          6.4978     8.3297
## parent_educsome college:practice_sportsometimes             2.7525     6.9253
## parent_educsome high school:practice_sportsometimes        -1.5359     6.5116
## parent_educbachelor's degree:is_first_childyes              5.9213     4.8829
## parent_educhigh school:is_first_childyes                    8.2978     4.1681
## parent_educmaster's degree:is_first_childyes                4.0575     7.2904
## parent_educsome college:is_first_childyes                  11.3686     4.0703
## parent_educsome high school:is_first_childyes               6.6910     4.0992
## parent_educbachelor's degree:transport_meansschool_bus      2.9865     4.8745
## parent_educhigh school:transport_meansschool_bus            4.2359     3.8916
## parent_educmaster's degree:transport_meansschool_bus        7.9641     6.0004
## parent_educsome college:transport_meansschool_bus           2.9693     3.9628
## parent_educsome high school:transport_meansschool_bus       6.6974     4.0323
## parent_educbachelor's degree:wkly_study_hours> 10         -10.0969     7.1918
## parent_educhigh school:wkly_study_hours> 10                -8.9401     5.9867
## parent_educmaster's degree:wkly_study_hours> 10            -0.4929    12.9542
## parent_educsome college:wkly_study_hours> 10               -7.9346     6.0260
## parent_educsome high school:wkly_study_hours> 10           -9.2345     6.1375
## parent_educbachelor's degree:wkly_study_hours10-May        -3.0831     4.9986
## parent_educhigh school:wkly_study_hours10-May             -11.4380     4.6604
## parent_educmaster's degree:wkly_study_hours10-May          -2.4586     6.6645
## parent_educsome college:wkly_study_hours10-May             -4.9978     4.7455
## parent_educsome high school:wkly_study_hours10-May         -9.0404     5.0069
## lunch_typestandard:test_prepnone                           -2.5751     2.9272
## lunch_typestandard:parent_marital_statusmarried            -7.6602     3.8303
## lunch_typestandard:parent_marital_statussingle             -4.8424     4.4351
## lunch_typestandard:parent_marital_statuswidowed            -0.3401    75.8094
## lunch_typestandard:practice_sportregularly                  9.3167     5.0489
## lunch_typestandard:practice_sportsometimes                 11.9692     4.8670
## lunch_typestandard:is_first_childyes                       -3.2287     2.9659
## lunch_typestandard:transport_meansschool_bus               -2.5877     2.7218
## lunch_typestandard:wkly_study_hours> 10                     6.6183     4.1533
## lunch_typestandard:wkly_study_hours10-May                   0.2394     3.1068
## test_prepnone:parent_marital_statusmarried                  1.3790     3.8961
## test_prepnone:parent_marital_statussingle                  -2.2649     4.4856
## test_prepnone:parent_marital_statuswidowed                -56.1241    39.6071
## test_prepnone:practice_sportregularly                       2.1756     4.8701
## test_prepnone:practice_sportsometimes                       4.8914     4.7728
## test_prepnone:is_first_childyes                            -0.6209     2.9395
## test_prepnone:transport_meansschool_bus                     2.2476     2.6727
## test_prepnone:wkly_study_hours> 10                         -2.8715     4.1954
## test_prepnone:wkly_study_hours10-May                        2.5604     3.3110
## parent_marital_statusmarried:practice_sportregularly        4.6749     6.2606
## parent_marital_statussingle:practice_sportregularly        -3.7080     8.1872
## parent_marital_statuswidowed:practice_sportregularly       -2.7432    80.1680
## parent_marital_statusmarried:practice_sportsometimes        2.9212     6.1741
## parent_marital_statussingle:practice_sportsometimes        -4.2724     8.0039
## parent_marital_statuswidowed:practice_sportsometimes            NA         NA
## parent_marital_statusmarried:is_first_childyes            -15.6491     4.6054
## parent_marital_statussingle:is_first_childyes              -7.5649     5.1042
## parent_marital_statuswidowed:is_first_childyes             39.8253    28.4103
## parent_marital_statusmarried:transport_meansschool_bus      4.5994     3.8033
## parent_marital_statussingle:transport_meansschool_bus       0.4248     4.3343
## parent_marital_statuswidowed:transport_meansschool_bus    -24.3230    18.4632
## parent_marital_statusmarried:wkly_study_hours> 10          19.5443     5.9414
## parent_marital_statussingle:wkly_study_hours> 10           25.1083     6.6075
## parent_marital_statuswidowed:wkly_study_hours> 10               NA         NA
## parent_marital_statusmarried:wkly_study_hours10-May         5.3774     4.3617
## parent_marital_statussingle:wkly_study_hours10-May          7.7403     4.8173
## parent_marital_statuswidowed:wkly_study_hours10-May             NA         NA
## practice_sportregularly:is_first_childyes                  -5.8879     5.6556
## practice_sportsometimes:is_first_childyes                  -7.2854     5.5185
## practice_sportregularly:transport_meansschool_bus           9.5708     4.7258
## practice_sportsometimes:transport_meansschool_bus           6.1714     4.5868
## practice_sportregularly:wkly_study_hours> 10                5.1152     6.7000
## practice_sportsometimes:wkly_study_hours> 10                3.1990     6.5717
## practice_sportregularly:wkly_study_hours10-May              6.9393     5.1561
## practice_sportsometimes:wkly_study_hours10-May             -0.3073     5.0837
## is_first_childyes:transport_meansschool_bus                -3.0863     2.8768
## is_first_childyes:wkly_study_hours> 10                      3.0112     4.3247
## is_first_childyes:wkly_study_hours10-May                   -2.5351     3.2646
## transport_meansschool_bus:wkly_study_hours> 10              2.0199     4.1559
## transport_meansschool_bus:wkly_study_hours10-May            1.8077     3.0009
##                                                           t value Pr(>|t|)    
## (Intercept)                                                 4.681 3.96e-06 ***
## gendermale                                                 -1.369 0.171871    
## ethnic_groupgroup B                                        -1.031 0.303382    
## ethnic_groupgroup C                                        -1.761 0.079032 .  
## ethnic_groupgroup D                                        -0.448 0.654545    
## ethnic_groupgroup E                                        -0.047 0.962465    
## parent_educbachelor's degree                                2.158 0.031556 *  
## parent_educhigh school                                      0.719 0.472484    
## parent_educmaster's degree                                 -0.652 0.514593    
## parent_educsome college                                    -0.758 0.448740    
## parent_educsome high school                                 0.033 0.973933    
## lunch_typestandard                                          0.371 0.710536    
## test_prepnone                                              -2.153 0.031925 *  
## parent_marital_statusmarried                                1.442 0.150115    
## parent_marital_statussingle                                 0.801 0.423760    
## parent_marital_statuswidowed                                1.099 0.272344    
## practice_sportregularly                                    -1.731 0.084330 .  
## practice_sportsometimes                                    -1.492 0.136489    
## is_first_childyes                                           1.481 0.139442    
## transport_meansschool_bus                                  -0.381 0.703477    
## wkly_study_hours> 10                                       -1.494 0.136054    
## wkly_study_hours10-May                                      0.158 0.874530    
## gendermale:ethnic_groupgroup B                              0.822 0.411462    
## gendermale:ethnic_groupgroup C                              1.813 0.070644 .  
## gendermale:ethnic_groupgroup D                              1.138 0.255657    
## gendermale:ethnic_groupgroup E                              0.937 0.349605    
## gendermale:parent_educbachelor's degree                    -0.707 0.479756    
## gendermale:parent_educhigh school                           0.290 0.772172    
## gendermale:parent_educmaster's degree                       1.576 0.115922    
## gendermale:parent_educsome college                         -1.073 0.283958    
## gendermale:parent_educsome high school                      0.067 0.946710    
## gendermale:lunch_typestandard                              -0.459 0.646819    
## gendermale:test_prepnone                                   -0.086 0.931825    
## gendermale:parent_marital_statusmarried                    -0.129 0.897232    
## gendermale:parent_marital_statussingle                     -0.036 0.971377    
## gendermale:parent_marital_statuswidowed                     0.071 0.943731    
## gendermale:practice_sportregularly                         -0.689 0.491428    
## gendermale:practice_sportsometimes                         -0.729 0.466204    
## gendermale:is_first_childyes                                1.108 0.268521    
## gendermale:transport_meansschool_bus                       -0.061 0.951464    
## gendermale:wkly_study_hours> 10                            -0.971 0.332150    
## gendermale:wkly_study_hours10-May                          -0.861 0.389706    
## ethnic_groupgroup B:parent_educbachelor's degree           -0.669 0.504113    
## ethnic_groupgroup C:parent_educbachelor's degree           -0.681 0.496462    
## ethnic_groupgroup D:parent_educbachelor's degree           -0.784 0.433391    
## ethnic_groupgroup E:parent_educbachelor's degree           -1.206 0.228465    
## ethnic_groupgroup B:parent_educhigh school                 -2.074 0.038774 *  
## ethnic_groupgroup C:parent_educhigh school                 -1.439 0.150891    
## ethnic_groupgroup D:parent_educhigh school                 -1.003 0.316603    
## ethnic_groupgroup E:parent_educhigh school                 -1.346 0.179020    
## ethnic_groupgroup B:parent_educmaster's degree              0.327 0.743685    
## ethnic_groupgroup C:parent_educmaster's degree             -0.537 0.591656    
## ethnic_groupgroup D:parent_educmaster's degree              0.205 0.837375    
## ethnic_groupgroup E:parent_educmaster's degree              0.092 0.927013    
## ethnic_groupgroup B:parent_educsome college                 0.372 0.709764    
## ethnic_groupgroup C:parent_educsome college                 0.734 0.463358    
## ethnic_groupgroup D:parent_educsome college                 1.128 0.260175    
## ethnic_groupgroup E:parent_educsome college                 0.303 0.761758    
## ethnic_groupgroup B:parent_educsome high school            -2.148 0.032364 *  
## ethnic_groupgroup C:parent_educsome high school            -1.338 0.181530    
## ethnic_groupgroup D:parent_educsome high school            -0.854 0.393676    
## ethnic_groupgroup E:parent_educsome high school            -0.517 0.605302    
## ethnic_groupgroup B:lunch_typestandard                      0.563 0.573723    
## ethnic_groupgroup C:lunch_typestandard                      1.285 0.199701    
## ethnic_groupgroup D:lunch_typestandard                      0.722 0.470435    
## ethnic_groupgroup E:lunch_typestandard                     -0.032 0.974675    
## ethnic_groupgroup B:test_prepnone                           0.428 0.669136    
## ethnic_groupgroup C:test_prepnone                           1.222 0.222374    
## ethnic_groupgroup D:test_prepnone                           0.805 0.421423    
## ethnic_groupgroup E:test_prepnone                           1.796 0.073229 .  
## ethnic_groupgroup B:parent_marital_statusmarried            0.529 0.596832    
## ethnic_groupgroup C:parent_marital_statusmarried           -0.033 0.973967    
## ethnic_groupgroup D:parent_marital_statusmarried           -1.569 0.117469    
## ethnic_groupgroup E:parent_marital_statusmarried           -0.572 0.567873    
## ethnic_groupgroup B:parent_marital_statussingle             1.163 0.245378    
## ethnic_groupgroup C:parent_marital_statussingle             0.248 0.803994    
## ethnic_groupgroup D:parent_marital_statussingle            -0.322 0.747428    
## ethnic_groupgroup E:parent_marital_statussingle             0.326 0.744500    
## ethnic_groupgroup B:parent_marital_statuswidowed            0.728 0.466816    
## ethnic_groupgroup C:parent_marital_statuswidowed            1.388 0.166042    
## ethnic_groupgroup D:parent_marital_statuswidowed            0.146 0.884212    
## ethnic_groupgroup E:parent_marital_statuswidowed               NA       NA    
## ethnic_groupgroup B:practice_sportregularly                 1.429 0.153942    
## ethnic_groupgroup C:practice_sportregularly                 1.587 0.113432    
## ethnic_groupgroup D:practice_sportregularly                 1.053 0.293000    
## ethnic_groupgroup E:practice_sportregularly                 1.260 0.208281    
## ethnic_groupgroup B:practice_sportsometimes                 1.166 0.244177    
## ethnic_groupgroup C:practice_sportsometimes                 2.096 0.036745 *  
## ethnic_groupgroup D:practice_sportsometimes                 1.043 0.297450    
## ethnic_groupgroup E:practice_sportsometimes                 1.184 0.237159    
## ethnic_groupgroup B:is_first_childyes                       1.732 0.084147 .  
## ethnic_groupgroup C:is_first_childyes                       0.650 0.516308    
## ethnic_groupgroup D:is_first_childyes                       0.347 0.728926    
## ethnic_groupgroup E:is_first_childyes                       0.447 0.654819    
## ethnic_groupgroup B:transport_meansschool_bus              -1.328 0.184937    
## ethnic_groupgroup C:transport_meansschool_bus              -2.169 0.030669 *  
## ethnic_groupgroup D:transport_meansschool_bus              -0.999 0.318358    
## ethnic_groupgroup E:transport_meansschool_bus              -1.970 0.049590 *  
## ethnic_groupgroup B:wkly_study_hours> 10                   -0.622 0.534294    
## ethnic_groupgroup C:wkly_study_hours> 10                    0.205 0.837996    
## ethnic_groupgroup D:wkly_study_hours> 10                    0.715 0.474919    
## ethnic_groupgroup E:wkly_study_hours> 10                    0.048 0.961392    
## ethnic_groupgroup B:wkly_study_hours10-May                 -0.722 0.471008    
## ethnic_groupgroup C:wkly_study_hours10-May                  0.234 0.814802    
## ethnic_groupgroup D:wkly_study_hours10-May                  0.369 0.712263    
## ethnic_groupgroup E:wkly_study_hours10-May                 -0.165 0.868800    
## parent_educbachelor's degree:lunch_typestandard             0.205 0.837509    
## parent_educhigh school:lunch_typestandard                   0.250 0.803050    
## parent_educmaster's degree:lunch_typestandard               0.975 0.329964    
## parent_educsome college:lunch_typestandard                  1.361 0.174329    
## parent_educsome high school:lunch_typestandard              1.421 0.156247    
## parent_educbachelor's degree:test_prepnone                 -0.294 0.768711    
## parent_educhigh school:test_prepnone                        0.432 0.666242    
## parent_educmaster's degree:test_prepnone                   -0.303 0.761677    
## parent_educsome college:test_prepnone                      -0.470 0.638759    
## parent_educsome high school:test_prepnone                   0.638 0.523982    
## parent_educbachelor's degree:parent_marital_statusmarried  -2.169 0.030688 *  
## parent_educhigh school:parent_marital_statusmarried         0.459 0.646215    
## parent_educmaster's degree:parent_marital_statusmarried     0.559 0.576337    
## parent_educsome college:parent_marital_statusmarried       -0.877 0.381080    
## parent_educsome high school:parent_marital_statusmarried   -0.703 0.482292    
## parent_educbachelor's degree:parent_marital_statussingle   -1.937 0.053489 .  
## parent_educhigh school:parent_marital_statussingle          1.062 0.288837    
## parent_educmaster's degree:parent_marital_statussingle      0.174 0.862019    
## parent_educsome college:parent_marital_statussingle        -0.758 0.448762    
## parent_educsome high school:parent_marital_statussingle    -0.619 0.536181    
## parent_educbachelor's degree:parent_marital_statuswidowed  -0.244 0.807209    
## parent_educhigh school:parent_marital_statuswidowed        -0.806 0.420742    
## parent_educmaster's degree:parent_marital_statuswidowed    -2.020 0.044071 *  
## parent_educsome college:parent_marital_statuswidowed       -1.435 0.152213    
## parent_educsome high school:parent_marital_statuswidowed   -0.846 0.398112    
## parent_educbachelor's degree:practice_sportregularly        0.226 0.821088    
## parent_educhigh school:practice_sportregularly             -1.551 0.121650    
## parent_educmaster's degree:practice_sportregularly          0.153 0.878559    
## parent_educsome college:practice_sportregularly            -0.021 0.983182    
## parent_educsome high school:practice_sportregularly        -0.471 0.637680    
## parent_educbachelor's degree:practice_sportsometimes       -1.060 0.289930    
## parent_educhigh school:practice_sportsometimes             -1.515 0.130609    
## parent_educmaster's degree:practice_sportsometimes          0.780 0.435832    
## parent_educsome college:practice_sportsometimes             0.397 0.691259    
## parent_educsome high school:practice_sportsometimes        -0.236 0.813660    
## parent_educbachelor's degree:is_first_childyes              1.213 0.226003    
## parent_educhigh school:is_first_childyes                    1.991 0.047213 *  
## parent_educmaster's degree:is_first_childyes                0.557 0.578162    
## parent_educsome college:is_first_childyes                   2.793 0.005483 ** 
## parent_educsome high school:is_first_childyes               1.632 0.103442    
## parent_educbachelor's degree:transport_meansschool_bus      0.613 0.540462    
## parent_educhigh school:transport_meansschool_bus            1.088 0.277080    
## parent_educmaster's degree:transport_meansschool_bus        1.327 0.185211    
## parent_educsome college:transport_meansschool_bus           0.749 0.454133    
## parent_educsome high school:transport_meansschool_bus       1.661 0.097541 .  
## parent_educbachelor's degree:wkly_study_hours> 10          -1.404 0.161148    
## parent_educhigh school:wkly_study_hours> 10                -1.493 0.136173    
## parent_educmaster's degree:wkly_study_hours> 10            -0.038 0.969667    
## parent_educsome college:wkly_study_hours> 10               -1.317 0.188716    
## parent_educsome high school:wkly_study_hours> 10           -1.505 0.133251    
## parent_educbachelor's degree:wkly_study_hours10-May        -0.617 0.537741    
## parent_educhigh school:wkly_study_hours10-May              -2.454 0.014560 *  
## parent_educmaster's degree:wkly_study_hours10-May          -0.369 0.712402    
## parent_educsome college:wkly_study_hours10-May             -1.053 0.292924    
## parent_educsome high school:wkly_study_hours10-May         -1.806 0.071766 .  
## lunch_typestandard:test_prepnone                           -0.880 0.379567    
## lunch_typestandard:parent_marital_statusmarried            -2.000 0.046216 *  
## lunch_typestandard:parent_marital_statussingle             -1.092 0.275596    
## lunch_typestandard:parent_marital_statuswidowed            -0.004 0.996423    
## lunch_typestandard:practice_sportregularly                  1.845 0.065767 .  
## lunch_typestandard:practice_sportsometimes                  2.459 0.014363 *  
## lunch_typestandard:is_first_childyes                       -1.089 0.277020    
## lunch_typestandard:transport_meansschool_bus               -0.951 0.342335    
## lunch_typestandard:wkly_study_hours> 10                     1.593 0.111876    
## lunch_typestandard:wkly_study_hours10-May                   0.077 0.938623    
## test_prepnone:parent_marital_statusmarried                  0.354 0.723573    
## test_prepnone:parent_marital_statussingle                  -0.505 0.613893    
## test_prepnone:parent_marital_statuswidowed                 -1.417 0.157290    
## test_prepnone:practice_sportregularly                       0.447 0.655333    
## test_prepnone:practice_sportsometimes                       1.025 0.306088    
## test_prepnone:is_first_childyes                            -0.211 0.832828    
## test_prepnone:transport_meansschool_bus                     0.841 0.400913    
## test_prepnone:wkly_study_hours> 10                         -0.684 0.494109    
## test_prepnone:wkly_study_hours10-May                        0.773 0.439827    
## parent_marital_statusmarried:practice_sportregularly        0.747 0.455689    
## parent_marital_statussingle:practice_sportregularly        -0.453 0.650870    
## parent_marital_statuswidowed:practice_sportregularly       -0.034 0.972721    
## parent_marital_statusmarried:practice_sportsometimes        0.473 0.636383    
## parent_marital_statussingle:practice_sportsometimes        -0.534 0.593797    
## parent_marital_statuswidowed:practice_sportsometimes           NA       NA    
## parent_marital_statusmarried:is_first_childyes             -3.398 0.000750 ***
## parent_marital_statussingle:is_first_childyes              -1.482 0.139140    
## parent_marital_statuswidowed:is_first_childyes              1.402 0.161788    
## parent_marital_statusmarried:transport_meansschool_bus      1.209 0.227285    
## parent_marital_statussingle:transport_meansschool_bus       0.098 0.921980    
## parent_marital_statuswidowed:transport_meansschool_bus     -1.317 0.188500    
## parent_marital_statusmarried:wkly_study_hours> 10           3.289 0.001097 ** 
## parent_marital_statussingle:wkly_study_hours> 10            3.800 0.000168 ***
## parent_marital_statuswidowed:wkly_study_hours> 10              NA       NA    
## parent_marital_statusmarried:wkly_study_hours10-May         1.233 0.218380    
## parent_marital_statussingle:wkly_study_hours10-May          1.607 0.108933    
## parent_marital_statuswidowed:wkly_study_hours10-May            NA       NA    
## practice_sportregularly:is_first_childyes                  -1.041 0.298498    
## practice_sportsometimes:is_first_childyes                  -1.320 0.187560    
## practice_sportregularly:transport_meansschool_bus           2.025 0.043539 *  
## practice_sportsometimes:transport_meansschool_bus           1.345 0.179276    
## practice_sportregularly:wkly_study_hours> 10                0.763 0.445653    
## practice_sportsometimes:wkly_study_hours> 10                0.487 0.626687    
## practice_sportregularly:wkly_study_hours10-May              1.346 0.179149    
## practice_sportsometimes:wkly_study_hours10-May             -0.060 0.951832    
## is_first_childyes:transport_meansschool_bus                -1.073 0.284019    
## is_first_childyes:wkly_study_hours> 10                      0.696 0.486682    
## is_first_childyes:wkly_study_hours10-May                   -0.777 0.437906    
## transport_meansschool_bus:wkly_study_hours> 10              0.486 0.627215    
## transport_meansschool_bus:wkly_study_hours10-May            0.602 0.547281    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 12.42 on 383 degrees of freedom
## Multiple R-squared:  0.5844, Adjusted R-squared:  0.3608 
## F-statistic: 2.614 on 206 and 383 DF,  p-value: 2.56e-16
stepwise_model_write <- step(full_fit_write, direction = "both", trace = 1)
## Start:  AIC=3131.41
## writing_score ~ (gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours)^2
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:test_prep                   5     245.4 59282 3123.9
## - ethnic_group:parent_educ               20    3361.8 62398 3124.1
## - gender:parent_marital_status            3       4.9 59041 3125.5
## - parent_educ:wkly_study_hours           10    1468.0 60504 3125.9
## - ethnic_group:wkly_study_hours           8    1092.4 60129 3126.2
## - parent_educ:transport_means             5     547.3 59583 3126.9
## - parent_marital_status:practice_sport    4     348.1 59384 3126.9
## - parent_educ:lunch_type                  5     600.2 59636 3127.4
## - transport_means:wkly_study_hours        2      63.5 59100 3128.1
## - gender:practice_sport                   2      85.6 59122 3128.3
## - ethnic_group:lunch_type                 4     513.8 59550 3128.5
## - parent_educ:parent_marital_status      13    2409.8 61446 3129.0
## - gender:wkly_study_hours                 2     167.8 59204 3129.1
## - gender:transport_means                  1       0.6 59037 3129.4
## - gender:test_prep                        1       1.1 59037 3129.4
## - test_prep:is_first_child                1       6.9 59043 3129.5
## - test_prep:parent_marital_status         2     211.7 59248 3129.5
## - gender:lunch_type                       1      32.4 59069 3129.7
## - test_prep:practice_sport                2     244.8 59281 3129.8
## - gender:ethnic_group                     4     652.4 59689 3129.9
## - gender:parent_educ                      5     856.7 59893 3129.9
## - practice_sport:is_first_child           2     277.0 59313 3130.2
## - test_prep:transport_means               1     109.0 59145 3130.5
## - lunch_type:test_prep                    1     119.3 59155 3130.6
## - lunch_type:transport_means              1     139.3 59176 3130.8
## - is_first_child:wkly_study_hours         2     340.9 59377 3130.8
## - ethnic_group:is_first_child             4     746.0 59782 3130.8
## - ethnic_group:test_prep                  4     757.2 59793 3130.9
## - is_first_child:transport_means          1     177.4 59214 3131.2
## - lunch_type:is_first_child               1     182.7 59219 3131.2
## - ethnic_group:practice_sport             8    1610.3 60646 3131.3
## - gender:is_first_child                   1     189.3 59225 3131.3
## - test_prep:wkly_study_hours              2     400.5 59437 3131.4
## <none>                                                59036 3131.4
## - parent_educ:practice_sport             10    2078.2 61114 3131.8
## - lunch_type:wkly_study_hours             2     509.7 59546 3132.5
## - parent_marital_status:transport_means   3     755.0 59791 3132.9
## - ethnic_group:parent_marital_status      9    1983.9 61020 3132.9
## - practice_sport:wkly_study_hours         4     995.1 60031 3133.3
## - lunch_type:parent_marital_status        2     650.3 59687 3133.9
## - practice_sport:transport_means          2     679.6 59716 3134.2
## - ethnic_group:transport_means            4    1108.7 60145 3134.4
## - parent_educ:is_first_child              5    1316.0 60352 3134.4
## - lunch_type:practice_sport               2     950.1 59986 3136.8
## - parent_marital_status:wkly_study_hours  4    2324.9 61361 3146.2
## - parent_marital_status:is_first_child    2    2312.7 61349 3150.1
## 
## Step:  AIC=3123.86
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:parent_educ + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     parent_educ:lunch_type + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:wkly_study_hours + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:parent_educ               20    3285.4 62567 3115.7
## - gender:parent_marital_status            3       7.5 59289 3117.9
## - ethnic_group:wkly_study_hours           8    1092.3 60374 3118.6
## - parent_marital_status:practice_sport    4     343.6 59625 3119.3
## - parent_educ:wkly_study_hours           10    1612.0 60894 3119.7
## - parent_educ:lunch_type                  5     596.6 59878 3119.8
## - parent_educ:transport_means             5     601.4 59883 3119.8
## - transport_means:wkly_study_hours        2      57.6 59339 3120.4
## - gender:practice_sport                   2      72.1 59354 3120.6
## - ethnic_group:lunch_type                 4     535.1 59817 3121.2
## - parent_educ:parent_marital_status      13    2393.4 61675 3121.2
## - gender:wkly_study_hours                 2     180.9 59462 3121.7
## - test_prep:parent_marital_status         2     184.5 59466 3121.7
## - gender:test_prep                        1       0.0 59282 3121.9
## - gender:transport_means                  1       1.8 59283 3121.9
## - test_prep:practice_sport                2     207.8 59489 3121.9
## - test_prep:is_first_child                1      10.7 59292 3122.0
## - gender:ethnic_group                     4     627.6 59909 3122.1
## - gender:lunch_type                       1      24.7 59306 3122.1
## - ethnic_group:test_prep                  4     639.2 59921 3122.2
## - gender:parent_educ                      5     892.7 60174 3122.7
## - test_prep:transport_means               1      98.8 59380 3122.8
## - is_first_child:wkly_study_hours         2     302.5 59584 3122.9
## - lunch_type:test_prep                    1     116.0 59398 3123.0
## - practice_sport:is_first_child           2     323.8 59605 3123.1
## - lunch_type:transport_means              1     133.6 59415 3123.2
## - gender:is_first_child                   1     166.6 59448 3123.5
## - ethnic_group:practice_sport             8    1607.5 60889 3123.6
## - ethnic_group:is_first_child             4     790.6 60072 3123.7
## - lunch_type:is_first_child               1     199.8 59481 3123.8
## <none>                                                59282 3123.9
## - is_first_child:transport_means          1     217.5 59499 3124.0
## - test_prep:wkly_study_hours              2     441.6 59723 3124.2
## - ethnic_group:parent_marital_status      9    1922.8 61204 3124.7
## - parent_educ:practice_sport             10    2157.5 61439 3124.9
## - lunch_type:wkly_study_hours             2     549.6 59831 3125.3
## - parent_marital_status:transport_means   3     758.5 60040 3125.4
## - lunch_type:parent_marital_status        2     587.8 59869 3125.7
## - practice_sport:wkly_study_hours         4    1017.6 60299 3125.9
## - ethnic_group:transport_means            4    1123.4 60405 3126.9
## - practice_sport:transport_means          2     729.9 60011 3127.1
## - parent_educ:is_first_child              5    1429.3 60711 3127.9
## - lunch_type:practice_sport               2     950.3 60232 3129.2
## + parent_educ:test_prep                   5     245.4 59036 3131.4
## - parent_marital_status:wkly_study_hours  4    2425.4 61707 3139.5
## - parent_marital_status:is_first_child    2    2368.4 61650 3143.0
## 
## Step:  AIC=3115.68
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     parent_educ:lunch_type + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:wkly_study_hours + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:wkly_study_hours           8     838.3 63405 3107.5
## - parent_educ:wkly_study_hours           10    1310.7 63878 3107.9
## - gender:parent_marital_status            3      12.5 62579 3109.8
## - parent_educ:lunch_type                  5     510.3 63077 3110.5
## - parent_marital_status:practice_sport    4     360.8 62928 3111.1
## - ethnic_group:practice_sport             8    1247.6 63815 3111.3
## - parent_educ:transport_means             5     641.0 63208 3111.7
## - gender:ethnic_group                     4     522.4 63089 3112.6
## - ethnic_group:test_prep                  4     527.3 63094 3112.6
## - test_prep:parent_marital_status         2     142.9 62710 3113.0
## - transport_means:wkly_study_hours        2     159.6 62726 3113.2
## - gender:wkly_study_hours                 2     161.7 62729 3113.2
## - gender:parent_educ                      5     828.0 63395 3113.4
## - gender:practice_sport                   2     190.3 62757 3113.5
## - is_first_child:wkly_study_hours         2     192.2 62759 3113.5
## - gender:transport_means                  1       0.9 62568 3113.7
## - gender:test_prep                        1       1.5 62568 3113.7
## - lunch_type:test_prep                    1       5.1 62572 3113.7
## - gender:lunch_type                       1       8.8 62576 3113.8
## - test_prep:practice_sport                2     223.8 62791 3113.8
## - parent_educ:parent_marital_status      13    2624.7 65192 3113.9
## - gender:is_first_child                   1      33.5 62600 3114.0
## - ethnic_group:lunch_type                 4     675.1 63242 3114.0
## - test_prep:is_first_child                1      43.5 62610 3114.1
## - practice_sport:is_first_child           2     284.8 62852 3114.4
## - lunch_type:parent_marital_status        2     286.8 62854 3114.4
## - test_prep:transport_means               1     107.4 62674 3114.7
## - parent_educ:practice_sport             10    2081.2 64648 3115.0
## - is_first_child:transport_means          1     173.0 62740 3115.3
## - lunch_type:is_first_child               1     198.5 62765 3115.6
## - parent_marital_status:transport_means   3     631.4 63198 3115.6
## <none>                                                62567 3115.7
## - lunch_type:transport_means              1     233.7 62801 3115.9
## - test_prep:wkly_study_hours              2     483.1 63050 3116.2
## - ethnic_group:is_first_child             4     945.3 63512 3116.5
## - practice_sport:transport_means          2     532.5 63099 3116.7
## - ethnic_group:transport_means            4     994.0 63561 3117.0
## - practice_sport:wkly_study_hours         4    1093.7 63661 3117.9
## - ethnic_group:parent_marital_status      9    2217.3 64784 3118.2
## - parent_educ:is_first_child              5    1371.0 63938 3118.5
## - lunch_type:wkly_study_hours             2     842.3 63409 3119.6
## - lunch_type:practice_sport               2    1121.1 63688 3122.2
## + ethnic_group:parent_educ               20    3285.4 59282 3123.9
## + parent_educ:test_prep                   5     169.0 62398 3124.1
## - parent_marital_status:wkly_study_hours  4    1981.5 64548 3126.1
## - parent_marital_status:is_first_child    2    2099.4 64666 3131.2
## 
## Step:  AIC=3107.54
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:lunch_type + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:wkly_study_hours + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:wkly_study_hours           10   1414.74 64820 3100.6
## - gender:parent_marital_status            3     21.12 63426 3101.7
## - parent_marital_status:practice_sport    4    273.36 63679 3102.1
## - parent_educ:lunch_type                  5    538.08 63943 3102.5
## - ethnic_group:practice_sport             8   1242.25 64647 3103.0
## - parent_educ:transport_means             5    629.09 64034 3103.4
## - transport_means:wkly_study_hours        2     74.29 63480 3104.2
## - gender:ethnic_group                     4    521.25 63926 3104.4
## - ethnic_group:test_prep                  4    528.77 63934 3104.4
## - parent_educ:parent_marital_status      13   2521.02 65926 3104.5
## - gender:wkly_study_hours                 2    111.28 63517 3104.6
## - test_prep:parent_marital_status         2    160.78 63566 3105.0
## - gender:parent_educ                      5    835.10 64240 3105.3
## - gender:practice_sport                   2    198.93 63604 3105.4
## - is_first_child:wkly_study_hours         2    202.74 63608 3105.4
## - lunch_type:test_prep                    1      0.02 63405 3105.5
## - gender:transport_means                  1      1.41 63407 3105.6
## - test_prep:practice_sport                2    223.33 63629 3105.6
## - gender:lunch_type                       1      9.19 63414 3105.6
## - gender:test_prep                        1     10.73 63416 3105.6
## - gender:is_first_child                   1     19.04 63424 3105.7
## - lunch_type:parent_marital_status        2    263.90 63669 3106.0
## - test_prep:is_first_child                1     61.13 63466 3106.1
## - test_prep:transport_means               1     83.82 63489 3106.3
## - ethnic_group:lunch_type                 4    737.87 64143 3106.4
## - practice_sport:is_first_child           2    307.72 63713 3106.4
## - parent_educ:practice_sport             10   2084.34 65490 3106.6
## - is_first_child:transport_means          1    182.81 63588 3107.2
## - lunch_type:transport_means              1    190.55 63596 3107.3
## <none>                                                63405 3107.5
## - lunch_type:is_first_child               1    222.45 63628 3107.6
## - parent_marital_status:transport_means   3    668.96 64074 3107.7
## - ethnic_group:is_first_child             4    906.30 64312 3107.9
## - test_prep:wkly_study_hours              2    479.44 63885 3108.0
## - practice_sport:transport_means          2    522.81 63928 3108.4
## - ethnic_group:transport_means            4   1002.86 64408 3108.8
## - ethnic_group:parent_marital_status      9   2134.54 65540 3109.1
## - parent_educ:is_first_child              5   1308.56 64714 3109.6
## - practice_sport:wkly_study_hours         4   1141.24 64546 3110.1
## - lunch_type:wkly_study_hours             2    905.28 64311 3111.9
## - lunch_type:practice_sport               2   1150.67 64556 3114.2
## + ethnic_group:wkly_study_hours           8    838.30 62567 3115.7
## + parent_educ:test_prep                   5    193.76 63211 3115.7
## - parent_marital_status:wkly_study_hours  4   1837.59 65243 3116.4
## + ethnic_group:parent_educ               20   3031.37 60374 3118.6
## - parent_marital_status:is_first_child    2   1979.54 65385 3121.7
## 
## Step:  AIC=3100.56
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:lunch_type + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:parent_marital_status            3      8.23 64828 3094.6
## - parent_educ:lunch_type                  5    450.88 65271 3094.7
## - ethnic_group:practice_sport             8   1175.09 65995 3095.2
## - parent_marital_status:practice_sport    4    329.09 65149 3095.5
## - parent_educ:transport_means             5    709.12 65529 3097.0
## - gender:ethnic_group                     4    488.42 65308 3097.0
## - ethnic_group:test_prep                  4    513.16 65333 3097.2
## - transport_means:wkly_study_hours        2    111.53 64932 3097.6
## - gender:parent_educ                      5    786.39 65606 3097.7
## - test_prep:parent_marital_status         2    128.82 64949 3097.7
## - is_first_child:wkly_study_hours         2    153.41 64973 3097.9
## - ethnic_group:lunch_type                 4    608.64 65429 3098.1
## - gender:practice_sport                   2    169.79 64990 3098.1
## - gender:transport_means                  1      0.57 64821 3098.6
## - lunch_type:test_prep                    1      2.61 64823 3098.6
## - gender:wkly_study_hours                 2    223.32 65043 3098.6
## - practice_sport:is_first_child           2    227.73 65048 3098.6
## - gender:lunch_type                       1      9.90 64830 3098.7
## - gender:test_prep                        1     17.01 64837 3098.7
## - gender:is_first_child                   1     29.46 64849 3098.8
## - test_prep:is_first_child                1     46.22 64866 3099.0
## - test_prep:practice_sport                2    284.13 65104 3099.1
## - lunch_type:parent_marital_status        2    297.47 65117 3099.3
## - test_prep:transport_means               1     90.44 64910 3099.4
## - parent_educ:parent_marital_status      13   2797.67 67618 3099.5
## - lunch_type:is_first_child               1    167.64 64988 3100.1
## - practice_sport:transport_means          2    388.54 65209 3100.1
## - is_first_child:transport_means          1    187.17 65007 3100.3
## <none>                                                64820 3100.6
## - ethnic_group:transport_means            4    890.45 65710 3100.6
## - practice_sport:wkly_study_hours         4    895.41 65715 3100.7
## - lunch_type:transport_means              1    231.07 65051 3100.7
## - parent_marital_status:transport_means   3    689.01 65509 3100.8
## - parent_educ:practice_sport             10   2285.42 67105 3101.0
## - ethnic_group:is_first_child             4    941.18 65761 3101.1
## - test_prep:wkly_study_hours              2    567.28 65387 3101.7
## - parent_educ:is_first_child              5   1260.35 66080 3101.9
## - lunch_type:wkly_study_hours             2    732.64 65553 3103.2
## - ethnic_group:parent_marital_status      9   2313.61 67134 3103.2
## - lunch_type:practice_sport               2   1122.55 65943 3106.7
## + parent_educ:wkly_study_hours           10   1414.74 63405 3107.5
## + ethnic_group:wkly_study_hours           8    942.30 63878 3107.9
## + parent_educ:test_prep                   5    254.90 64565 3108.2
## - parent_marital_status:wkly_study_hours  4   2025.70 66846 3110.7
## + ethnic_group:parent_educ               20   2750.70 62069 3115.0
## - parent_marital_status:is_first_child    2   2080.59 66901 3115.2
## 
## Step:  AIC=3094.63
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:practice_sport + gender:is_first_child + gender:transport_means + 
##     gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:parent_marital_status + ethnic_group:practice_sport + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:lunch_type + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:lunch_type                  5    453.76 65282 3088.8
## - ethnic_group:practice_sport             8   1171.59 66000 3089.2
## - parent_marital_status:practice_sport    4    327.63 65156 3089.6
## - parent_educ:transport_means             5    704.99 65533 3091.0
## - gender:ethnic_group                     4    484.60 65313 3091.0
## - ethnic_group:test_prep                  4    518.12 65346 3091.3
## - transport_means:wkly_study_hours        2    112.25 64940 3091.7
## - test_prep:parent_marital_status         2    129.44 64958 3091.8
## - gender:parent_educ                      5    802.53 65631 3091.9
## - is_first_child:wkly_study_hours         2    150.98 64979 3092.0
## - ethnic_group:lunch_type                 4    611.63 65440 3092.2
## - gender:practice_sport                   2    175.34 65004 3092.2
## - gender:transport_means                  1      0.68 64829 3092.6
## - lunch_type:test_prep                    1      2.43 64831 3092.7
## - practice_sport:is_first_child           2    227.81 65056 3092.7
## - gender:lunch_type                       1      9.03 64837 3092.7
## - gender:wkly_study_hours                 2    232.70 65061 3092.7
## - gender:test_prep                        1     17.92 64846 3092.8
## - gender:is_first_child                   1     32.58 64861 3092.9
## - test_prep:is_first_child                1     46.46 64875 3093.1
## - test_prep:practice_sport                2    295.19 65123 3093.3
## - test_prep:transport_means               1     89.71 64918 3093.4
## - lunch_type:parent_marital_status        2    325.21 65153 3093.6
## - parent_educ:parent_marital_status      13   2846.27 67674 3094.0
## - practice_sport:transport_means          2    384.18 65212 3094.1
## - lunch_type:is_first_child               1    169.80 64998 3094.2
## - is_first_child:transport_means          1    197.72 65026 3094.4
## <none>                                                64828 3094.6
## - ethnic_group:transport_means            4    891.25 65719 3094.7
## - lunch_type:transport_means              1    237.39 65066 3094.8
## - practice_sport:wkly_study_hours         4    914.03 65742 3094.9
## - ethnic_group:is_first_child             4    941.88 65770 3095.1
## - parent_educ:practice_sport             10   2323.35 67152 3095.4
## - test_prep:wkly_study_hours              2    565.73 65394 3095.8
## - parent_marital_status:transport_means   3    799.54 65628 3095.9
## - parent_educ:is_first_child              5   1262.58 66091 3096.0
## - lunch_type:wkly_study_hours             2    745.49 65574 3097.4
## - ethnic_group:parent_marital_status      9   2441.41 67270 3098.4
## + gender:parent_marital_status            3      8.23 64820 3100.6
## - lunch_type:practice_sport               2   1165.09 65993 3101.1
## + parent_educ:wkly_study_hours           10   1401.85 63426 3101.7
## + ethnic_group:wkly_study_hours           8    943.83 63884 3102.0
## + parent_educ:test_prep                   5    256.20 64572 3102.3
## - parent_marital_status:wkly_study_hours  4   2029.22 66857 3104.8
## + ethnic_group:parent_educ               20   2749.68 62079 3109.1
## - parent_marital_status:is_first_child    2   2115.57 66944 3109.6
## 
## Step:  AIC=3088.75
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:practice_sport + gender:is_first_child + gender:transport_means + 
##     gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:parent_marital_status + ethnic_group:practice_sport + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:practice_sport             8   1102.72 66385 3082.6
## - parent_marital_status:practice_sport    4    362.52 65644 3084.0
## - gender:ethnic_group                     4    473.96 65756 3085.0
## - parent_educ:transport_means             5    705.99 65988 3085.1
## - gender:parent_educ                      5    730.18 66012 3085.3
## - ethnic_group:test_prep                  4    552.03 65834 3085.7
## - test_prep:parent_marital_status         2    124.91 65407 3085.9
## - transport_means:wkly_study_hours        2    125.88 65408 3085.9
## - ethnic_group:lunch_type                 4    589.22 65871 3086.1
## - is_first_child:wkly_study_hours         2    147.84 65430 3086.1
## - gender:practice_sport                   2    177.50 65459 3086.3
## - gender:wkly_study_hours                 2    210.11 65492 3086.6
## - gender:transport_means                  1      0.48 65282 3086.8
## - lunch_type:test_prep                    1      3.83 65286 3086.8
## - gender:test_prep                        1     15.37 65297 3086.9
## - practice_sport:is_first_child           2    240.28 65522 3086.9
## - gender:lunch_type                       1     24.06 65306 3087.0
## - test_prep:is_first_child                1     34.65 65317 3087.1
## - gender:is_first_child                   1     64.33 65346 3087.3
## - lunch_type:parent_marital_status        2    294.12 65576 3087.4
## - test_prep:transport_means               1    113.55 65396 3087.8
## - test_prep:practice_sport                2    351.93 65634 3087.9
## - lunch_type:is_first_child               1    140.20 65422 3088.0
## - ethnic_group:transport_means            4    848.96 66131 3088.4
## - is_first_child:transport_means          1    183.22 65465 3088.4
## <none>                                                65282 3088.8
## - practice_sport:transport_means          2    445.89 65728 3088.8
## - parent_educ:parent_marital_status      13   2963.47 68245 3088.9
## - lunch_type:transport_means              1    274.34 65556 3089.2
## - ethnic_group:is_first_child             4    953.00 66235 3089.3
## - practice_sport:wkly_study_hours         4    967.93 66250 3089.4
## - parent_educ:practice_sport             10   2339.85 67622 3089.5
## - parent_educ:is_first_child              5   1226.98 66509 3089.7
## - test_prep:wkly_study_hours              2    569.64 65852 3089.9
## - parent_marital_status:transport_means   3    859.31 66141 3090.5
## - lunch_type:wkly_study_hours             2    714.94 65997 3091.2
## - ethnic_group:parent_marital_status      9   2385.39 67667 3091.9
## + parent_educ:lunch_type                  5    453.76 64828 3094.6
## + gender:parent_marital_status            3     11.11 65271 3094.7
## - lunch_type:practice_sport               2   1117.40 66399 3094.8
## + ethnic_group:wkly_study_hours           8    944.83 64337 3096.1
## + parent_educ:wkly_study_hours           10   1311.24 63971 3096.8
## + parent_educ:test_prep                   5    207.94 65074 3096.9
## - parent_marital_status:wkly_study_hours  4   2112.97 67395 3099.5
## + ethnic_group:parent_educ               20   2782.22 62500 3103.1
## - parent_marital_status:is_first_child    2   2274.32 67556 3104.9
## 
## Step:  AIC=3082.63
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:practice_sport + gender:is_first_child + gender:transport_means + 
##     gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:ethnic_group                     4    334.06 66719 3077.6
## - parent_educ:transport_means             5    602.59 66987 3078.0
## - gender:parent_educ                      5    667.19 67052 3078.5
## - parent_marital_status:practice_sport    4    536.65 66921 3079.4
## - ethnic_group:test_prep                  4    578.24 66963 3079.8
## - practice_sport:is_first_child           2    144.13 66529 3079.9
## - test_prep:parent_marital_status         2    152.27 66537 3080.0
## - transport_means:wkly_study_hours        2    160.57 66545 3080.1
## - is_first_child:wkly_study_hours         2    164.84 66550 3080.1
## - gender:transport_means                  1      1.29 66386 3080.6
## - gender:test_prep                        1      5.51 66390 3080.7
## - gender:lunch_type                       1     10.61 66395 3080.7
## - ethnic_group:lunch_type                 4    704.57 67089 3080.9
## - test_prep:is_first_child                1     28.20 66413 3080.9
## - gender:is_first_child                   1     30.57 66415 3080.9
## - lunch_type:test_prep                    1     31.63 66416 3080.9
## - test_prep:practice_sport                2    289.60 66674 3081.2
## - gender:wkly_study_hours                 2    292.89 66678 3081.2
## - lunch_type:parent_marital_status        2    313.74 66698 3081.4
## - parent_educ:parent_marital_status      13   2856.05 69241 3081.5
## - gender:practice_sport                   2    329.64 66714 3081.6
## - test_prep:transport_means               1    123.71 66508 3081.7
## - ethnic_group:is_first_child             4    851.65 67236 3082.2
## - ethnic_group:transport_means            4    854.21 67239 3082.2
## - lunch_type:is_first_child               1    178.29 66563 3082.2
## - practice_sport:transport_means          2    413.68 66798 3082.3
## - lunch_type:transport_means              1    210.36 66595 3082.5
## <none>                                                66385 3082.6
## - is_first_child:transport_means          1    226.07 66611 3082.6
## - test_prep:wkly_study_hours              2    457.36 66842 3082.7
## - practice_sport:wkly_study_hours         4    926.35 67311 3082.8
## - parent_educ:practice_sport             10   2400.56 68785 3083.6
## - parent_educ:is_first_child              5   1378.21 67763 3084.8
## - parent_marital_status:transport_means   3    938.11 67323 3084.9
## - lunch_type:wkly_study_hours             2    734.78 67119 3085.1
## - ethnic_group:parent_marital_status      9   2431.75 68816 3085.8
## - lunch_type:practice_sport               2   1041.78 67426 3087.8
## + gender:parent_marital_status            3      8.49 66376 3088.6
## + ethnic_group:practice_sport             8   1102.72 65282 3088.8
## + parent_educ:lunch_type                  5    384.89 66000 3089.2
## + ethnic_group:wkly_study_hours           8    970.65 65414 3089.9
## + parent_educ:test_prep                   5    200.85 66184 3090.8
## + parent_educ:wkly_study_hours           10   1239.53 65145 3091.5
## - parent_marital_status:wkly_study_hours  4   2251.07 68636 3094.3
## - parent_marital_status:is_first_child    2   2096.19 68481 3097.0
## + ethnic_group:parent_educ               20   2346.89 64038 3101.4
## 
## Step:  AIC=3077.59
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:parent_educ + 
##     gender:lunch_type + gender:test_prep + gender:practice_sport + 
##     gender:is_first_child + gender:transport_means + gender:wkly_study_hours + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:transport_means             5    543.87 67263 3072.4
## - gender:parent_educ                      5    573.95 67293 3072.6
## - ethnic_group:test_prep                  4    502.89 67222 3074.0
## - parent_marital_status:practice_sport    4    539.12 67258 3074.3
## - test_prep:parent_marital_status         2    143.84 66863 3074.9
## - is_first_child:wkly_study_hours         2    166.05 66885 3075.1
## - practice_sport:is_first_child           2    168.91 66888 3075.1
## - transport_means:wkly_study_hours        2    184.33 66903 3075.2
## - gender:transport_means                  1      0.05 66719 3075.6
## - gender:test_prep                        1      4.59 66723 3075.6
## - gender:lunch_type                       1      8.88 66728 3075.7
## - ethnic_group:lunch_type                 4    701.29 67420 3075.8
## - test_prep:is_first_child                1     27.50 66746 3075.8
## - gender:is_first_child                   1     37.57 66756 3075.9
## - lunch_type:test_prep                    1     42.48 66761 3076.0
## - test_prep:practice_sport                2    284.58 67003 3076.1
## - lunch_type:parent_marital_status        2    300.95 67020 3076.2
## - gender:practice_sport                   2    316.56 67035 3076.4
## - gender:wkly_study_hours                 2    323.72 67042 3076.4
## - test_prep:transport_means               1    136.37 66855 3076.8
## - parent_educ:parent_marital_status      13   2927.80 69647 3076.9
## - ethnic_group:is_first_child             4    837.49 67556 3076.9
## - ethnic_group:transport_means            4    843.50 67562 3077.0
## - practice_sport:transport_means          2    404.91 67124 3077.2
## - lunch_type:is_first_child               1    185.14 66904 3077.2
## - lunch_type:transport_means              1    215.15 66934 3077.5
## <none>                                                66719 3077.6
## - is_first_child:transport_means          1    247.01 66966 3077.8
## - test_prep:wkly_study_hours              2    499.70 67218 3078.0
## - practice_sport:wkly_study_hours         4    963.49 67682 3078.1
## - parent_educ:practice_sport             10   2429.40 69148 3078.7
## - ethnic_group:parent_marital_status      9   2321.43 69040 3079.8
## - parent_marital_status:transport_means   3    952.44 67671 3079.9
## - lunch_type:wkly_study_hours             2    735.88 67455 3080.1
## - parent_educ:is_first_child              5   1473.91 68193 3080.5
## + gender:ethnic_group                     4    334.06 66385 3082.6
## + gender:parent_marital_status            3      9.39 66709 3083.5
## - lunch_type:practice_sport               2   1175.07 67894 3083.9
## + parent_educ:lunch_type                  5    385.08 66334 3084.2
## + ethnic_group:wkly_study_hours           8    973.05 65746 3084.9
## + ethnic_group:practice_sport             8    962.81 65756 3085.0
## + parent_educ:test_prep                   5    159.07 66560 3086.2
## + parent_educ:wkly_study_hours           10   1225.64 65493 3086.7
## - parent_marital_status:wkly_study_hours  4   2289.79 69009 3089.5
## - parent_marital_status:is_first_child    2   2193.29 68912 3092.7
## + ethnic_group:parent_educ               20   2280.02 64439 3097.1
## 
## Step:  AIC=3072.38
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:parent_educ + 
##     gender:lunch_type + gender:test_prep + gender:practice_sport + 
##     gender:is_first_child + gender:transport_means + gender:wkly_study_hours + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:parent_educ                      5    579.12 67842 3067.4
## - ethnic_group:test_prep                  4    537.48 67800 3069.1
## - parent_marital_status:practice_sport    4    539.25 67802 3069.1
## - test_prep:parent_marital_status         2    134.95 67398 3069.6
## - practice_sport:is_first_child           2    135.32 67398 3069.6
## - is_first_child:wkly_study_hours         2    153.61 67416 3069.7
## - transport_means:wkly_study_hours        2    184.05 67447 3070.0
## - gender:transport_means                  1      0.09 67263 3070.4
## - gender:test_prep                        1      1.81 67264 3070.4
## - gender:lunch_type                       1     15.08 67278 3070.5
## - gender:is_first_child                   1     33.95 67297 3070.7
## - gender:wkly_study_hours                 2    266.92 67530 3070.7
## - test_prep:is_first_child                1     50.08 67313 3070.8
## - lunch_type:test_prep                    1     58.79 67321 3070.9
## - test_prep:practice_sport                2    301.02 67564 3071.0
## - ethnic_group:lunch_type                 4    765.58 68028 3071.1
## - practice_sport:transport_means          2    331.21 67594 3071.3
## - parent_educ:parent_marital_status      13   2920.47 70183 3071.5
## - gender:practice_sport                   2    354.13 67617 3071.5
## - lunch_type:parent_marital_status        2    356.61 67619 3071.5
## - test_prep:transport_means               1    161.49 67424 3071.8
## - ethnic_group:is_first_child             4    860.27 68123 3071.9
## - lunch_type:is_first_child               1    192.18 67455 3072.1
## - is_first_child:transport_means          1    210.90 67474 3072.2
## - lunch_type:transport_means              1    213.26 67476 3072.2
## <none>                                                67263 3072.4
## - ethnic_group:transport_means            4    960.94 68224 3072.8
## - test_prep:wkly_study_hours              2    521.24 67784 3072.9
## - parent_educ:practice_sport             10   2393.16 69656 3073.0
## - practice_sport:wkly_study_hours         4   1070.29 68333 3073.7
## - parent_marital_status:transport_means   3    845.76 68108 3073.8
## - parent_educ:is_first_child              5   1453.38 68716 3075.0
## - ethnic_group:parent_marital_status      9   2419.49 69682 3075.2
## - lunch_type:wkly_study_hours             2    855.76 68118 3075.8
## + parent_educ:transport_means             5    543.87 66719 3077.6
## + gender:ethnic_group                     4    275.34 66987 3078.0
## + gender:parent_marital_status            3     15.46 67247 3078.2
## + parent_educ:lunch_type                  5    384.38 66878 3079.0
## - lunch_type:practice_sport               2   1273.57 68536 3079.4
## + ethnic_group:wkly_study_hours           8    916.36 66346 3080.3
## + parent_educ:test_prep                   5    205.37 67057 3080.6
## + ethnic_group:practice_sport             8    878.28 66384 3080.6
## + parent_educ:wkly_study_hours           10   1247.47 66015 3081.3
## - parent_marital_status:wkly_study_hours  4   2322.31 69585 3084.4
## - parent_marital_status:is_first_child    2   2177.48 69440 3087.2
## + ethnic_group:parent_educ               20   2463.59 64799 3090.4
## 
## Step:  AIC=3067.44
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:test_prep                  4     472.9 68315 3063.5
## - parent_marital_status:practice_sport    4     538.6 68380 3064.1
## - test_prep:parent_marital_status         2     116.3 67958 3064.4
## - practice_sport:is_first_child           2     164.3 68006 3064.9
## - is_first_child:wkly_study_hours         2     175.1 68017 3065.0
## - transport_means:wkly_study_hours        2     188.2 68030 3065.1
## - gender:transport_means                  1       0.1 67842 3065.4
## - gender:test_prep                        1       1.5 67843 3065.4
## - ethnic_group:lunch_type                 4     700.2 68542 3065.5
## - gender:lunch_type                       1      16.1 67858 3065.6
## - gender:is_first_child                   1      34.3 67876 3065.7
## - gender:wkly_study_hours                 2     295.8 68138 3066.0
## - practice_sport:transport_means          2     303.3 68145 3066.1
## - test_prep:is_first_child                1      73.1 67915 3066.1
## - lunch_type:test_prep                    1      80.4 67922 3066.1
## - lunch_type:parent_marital_status        2     345.7 68187 3066.4
## - test_prep:practice_sport                2     352.4 68194 3066.5
## - gender:practice_sport                   2     362.5 68204 3066.6
## - test_prep:transport_means               1     158.6 68000 3066.8
## - ethnic_group:is_first_child             4     855.9 68698 3066.8
## - is_first_child:transport_means          1     195.1 68037 3067.1
## - lunch_type:is_first_child               1     204.2 68046 3067.2
## <none>                                                67842 3067.4
## - parent_educ:practice_sport             10    2394.3 70236 3067.9
## - lunch_type:transport_means              1     288.9 68131 3067.9
## - test_prep:wkly_study_hours              2     576.3 68418 3068.4
## - practice_sport:wkly_study_hours         4    1062.6 68904 3068.6
## - parent_educ:is_first_child              5    1333.5 69175 3068.9
## - parent_educ:parent_marital_status      13    3262.6 71104 3069.2
## - ethnic_group:transport_means            4    1140.1 68982 3069.3
## - parent_marital_status:transport_means   3     926.1 68768 3069.4
## - ethnic_group:parent_marital_status      9    2363.8 70206 3069.7
## - lunch_type:wkly_study_hours             2     879.5 68721 3071.0
## + gender:parent_educ                      5     579.1 67263 3072.4
## + parent_educ:transport_means             5     549.0 67293 3072.6
## + gender:parent_marital_status            3       4.7 67837 3073.4
## + gender:ethnic_group                     4     194.0 67648 3073.8
## + parent_educ:lunch_type                  5     343.0 67499 3074.4
## - lunch_type:practice_sport               2    1328.3 69170 3074.9
## + ethnic_group:wkly_study_hours           8     895.6 66946 3075.6
## + parent_educ:test_prep                   5     172.0 67670 3075.9
## + ethnic_group:practice_sport             8     845.9 66996 3076.0
## + parent_educ:wkly_study_hours           10    1223.0 66619 3076.7
## - parent_marital_status:wkly_study_hours  4    2407.9 70250 3080.0
## - parent_marital_status:is_first_child    2    2111.7 69953 3081.5
## + ethnic_group:parent_educ               20    2467.1 65375 3085.6
## 
## Step:  AIC=3063.54
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_marital_status:practice_sport    4     515.8 68830 3060.0
## - test_prep:parent_marital_status         2     135.4 68450 3060.7
## - ethnic_group:lunch_type                 4     622.0 68937 3060.9
## - is_first_child:wkly_study_hours         2     165.2 68480 3061.0
## - transport_means:wkly_study_hours        2     186.3 68501 3061.1
## - practice_sport:is_first_child           2     200.7 68515 3061.3
## - gender:test_prep                        1       0.1 68315 3061.5
## - gender:transport_means                  1       0.1 68315 3061.5
## - gender:lunch_type                       1       9.7 68324 3061.6
## - gender:is_first_child                   1      17.5 68332 3061.7
## - test_prep:practice_sport                2     287.2 68602 3062.0
## - test_prep:is_first_child                1      69.2 68384 3062.1
## - gender:wkly_study_hours                 2     303.9 68619 3062.2
## - practice_sport:transport_means          2     316.7 68631 3062.3
## - lunch_type:test_prep                    1     103.0 68418 3062.4
## - gender:practice_sport                   2     362.7 68677 3062.7
## - lunch_type:parent_marital_status        2     373.3 68688 3062.8
## - ethnic_group:is_first_child             4     849.9 69165 3062.8
## - test_prep:transport_means               1     196.2 68511 3063.2
## - is_first_child:transport_means          1     200.9 68515 3063.3
## - lunch_type:is_first_child               1     207.4 68522 3063.3
## <none>                                                68315 3063.5
## - parent_educ:practice_sport             10    2386.3 70701 3063.8
## - lunch_type:transport_means              1     325.6 68640 3064.3
## - practice_sport:wkly_study_hours         4    1079.2 69394 3064.8
## - parent_educ:is_first_child              5    1328.6 69643 3064.9
## - test_prep:wkly_study_hours              2     642.6 68957 3065.1
## - parent_educ:parent_marital_status      13    3270.8 71585 3065.1
## - parent_marital_status:transport_means   3     893.5 69208 3065.2
## - ethnic_group:parent_marital_status      9    2398.8 70713 3065.9
## - ethnic_group:transport_means            4    1216.2 69531 3065.9
## - lunch_type:wkly_study_hours             2     883.9 69199 3067.1
## + ethnic_group:test_prep                  4     472.9 67842 3067.4
## + parent_educ:transport_means             5     580.8 67734 3068.5
## + gender:parent_educ                      5     514.5 67800 3069.1
## + gender:parent_marital_status            3       4.7 68310 3069.5
## + gender:ethnic_group                     4     157.4 68157 3070.2
## + parent_educ:lunch_type                  5     352.3 67962 3070.5
## + ethnic_group:wkly_study_hours           8     891.3 67423 3071.8
## - lunch_type:practice_sport               2    1447.4 69762 3071.9
## + ethnic_group:practice_sport             8     870.0 67445 3072.0
## + parent_educ:wkly_study_hours           10    1235.0 67080 3072.8
## + parent_educ:test_prep                   5      87.1 68228 3072.8
## - parent_marital_status:wkly_study_hours  4    2256.3 70571 3074.7
## - parent_marital_status:is_first_child    2    2108.8 70423 3077.5
## + ethnic_group:parent_educ               20    2467.3 65847 3081.8
## 
## Step:  AIC=3059.97
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:parent_marital_status         2     118.5 68949 3057.0
## - practice_sport:is_first_child           2     135.1 68966 3057.1
## - lunch_type:parent_marital_status        3     380.8 69211 3057.2
## - transport_means:wkly_study_hours        2     180.1 69011 3057.5
## - is_first_child:wkly_study_hours         2     208.2 69039 3057.8
## - ethnic_group:lunch_type                 4     693.2 69524 3057.9
## - gender:transport_means                  1       0.1 68831 3058.0
## - gender:test_prep                        1       1.6 68832 3058.0
## - gender:is_first_child                   1      10.6 68841 3058.1
## - gender:lunch_type                       1      11.7 68842 3058.1
## - practice_sport:transport_means          2     277.5 69108 3058.3
## - test_prep:practice_sport                2     288.4 69119 3058.4
## - test_prep:is_first_child                1      63.3 68894 3058.5
## - gender:wkly_study_hours                 2     335.4 69166 3058.8
## - lunch_type:test_prep                    1     108.8 68939 3058.9
## - lunch_type:is_first_child               1     147.8 68978 3059.2
## - ethnic_group:is_first_child             4     868.0 69698 3059.4
## - gender:practice_sport                   2     400.2 69231 3059.4
## - test_prep:transport_means               1     173.0 69003 3059.5
## - parent_educ:practice_sport             10    2335.4 71166 3059.7
## - is_first_child:transport_means          1     222.7 69053 3059.9
## <none>                                                68830 3060.0
## - lunch_type:transport_means              1     270.9 69101 3060.3
## - ethnic_group:parent_marital_status     10    2412.2 71243 3060.3
## - parent_educ:is_first_child              5    1324.6 70155 3061.2
## - practice_sport:wkly_study_hours         4    1108.8 69939 3061.4
## - parent_marital_status:transport_means   3     877.4 69708 3061.4
## - ethnic_group:transport_means            4    1123.2 69954 3061.5
## - test_prep:wkly_study_hours              2     713.3 69544 3062.1
## - parent_educ:parent_marital_status      14    3646.4 72477 3062.4
## - lunch_type:wkly_study_hours             2     867.7 69698 3063.4
## + parent_marital_status:practice_sport    4     515.8 68315 3063.5
## + ethnic_group:test_prep                  4     450.1 68380 3064.1
## + parent_educ:transport_means             5     597.6 68233 3064.8
## + gender:parent_educ                      5     512.3 68318 3065.6
## + gender:parent_marital_status            3       3.7 68827 3065.9
## + gender:ethnic_group                     4     171.0 68659 3066.5
## + parent_educ:lunch_type                  5     376.4 68454 3066.7
## + ethnic_group:practice_sport             8     991.3 67839 3067.4
## - lunch_type:practice_sport               2    1394.4 70225 3067.8
## + parent_educ:wkly_study_hours           10    1326.5 67504 3068.5
## + parent_educ:test_prep                   5      91.2 68739 3069.2
## + ethnic_group:wkly_study_hours           8     764.8 68066 3069.4
## - parent_marital_status:wkly_study_hours  5    2336.3 71167 3069.7
## - parent_marital_status:is_first_child    2    2343.8 71174 3075.7
## + ethnic_group:parent_educ               20    2528.6 66302 3077.9
## 
## Step:  AIC=3056.99
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:parent_marital_status        3     363.1 69312 3054.1
## - practice_sport:is_first_child           2     128.7 69078 3054.1
## - transport_means:wkly_study_hours        2     187.6 69137 3054.6
## - is_first_child:wkly_study_hours         2     219.9 69169 3054.9
## - gender:transport_means                  1       0.0 68949 3055.0
## - gender:test_prep                        1       0.9 68950 3055.0
## - ethnic_group:lunch_type                 4     708.8 69658 3055.0
## - gender:is_first_child                   1      12.3 68961 3055.1
## - gender:lunch_type                       1      13.4 68962 3055.1
## - practice_sport:transport_means          2     279.0 69228 3055.4
## - test_prep:practice_sport                2     309.6 69259 3055.6
## - test_prep:is_first_child                1      81.0 69030 3055.7
## - gender:wkly_study_hours                 2     339.7 69289 3055.9
## - ethnic_group:parent_marital_status     11    2493.0 71442 3055.9
## - lunch_type:test_prep                    1     116.7 69066 3056.0
## - lunch_type:is_first_child               1     130.3 69079 3056.1
## - gender:practice_sport                   2     390.2 69339 3056.3
## - test_prep:transport_means               1     190.2 69139 3056.6
## - parent_educ:practice_sport             10    2364.1 71313 3056.9
## - is_first_child:transport_means          1     221.4 69170 3056.9
## <none>                                                68949 3057.0
## - ethnic_group:is_first_child             4     941.5 69890 3057.0
## - lunch_type:transport_means              1     271.5 69221 3057.3
## - practice_sport:wkly_study_hours         4    1068.4 70017 3058.1
## - parent_educ:parent_marital_status      15    3736.4 72685 3058.1
## - parent_educ:is_first_child              5    1326.1 70275 3058.2
## - ethnic_group:transport_means            4    1133.8 70083 3058.6
## - parent_marital_status:transport_means   3     949.4 69898 3059.1
## - test_prep:wkly_study_hours              2     717.9 69667 3059.1
## + test_prep:parent_marital_status         2     118.5 68830 3060.0
## - lunch_type:wkly_study_hours             2     854.3 69803 3060.3
## + parent_marital_status:practice_sport    4     498.9 68450 3060.7
## + ethnic_group:test_prep                  4     471.9 68477 3060.9
## + parent_educ:transport_means             5     594.1 68355 3061.9
## + gender:parent_educ                      5     487.7 68461 3062.8
## + gender:parent_marital_status            3       3.2 68946 3063.0
## + gender:ethnic_group                     4     173.1 68776 3063.5
## + parent_educ:lunch_type                  5     381.0 68568 3063.7
## + ethnic_group:practice_sport             8    1010.9 67938 3064.3
## - lunch_type:practice_sport               2    1364.2 70313 3064.6
## + parent_educ:wkly_study_hours           10    1310.2 67639 3065.7
## + ethnic_group:wkly_study_hours           8     808.1 68141 3066.0
## + parent_educ:test_prep                   5      83.1 68866 3066.3
## - parent_marital_status:wkly_study_hours  6    2636.8 71586 3067.1
## - parent_marital_status:is_first_child    3    2492.4 71441 3071.9
## + ethnic_group:parent_educ               20    2530.7 66418 3074.9
## 
## Step:  AIC=3054.09
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - practice_sport:is_first_child           2     102.1 69414 3051.0
## - is_first_child:wkly_study_hours         2     207.0 69519 3051.8
## - ethnic_group:parent_marital_status     11    2366.0 71678 3051.9
## - transport_means:wkly_study_hours        2     212.7 69525 3051.9
## - gender:transport_means                  1       1.3 69313 3052.1
## - gender:test_prep                        1       3.7 69316 3052.1
## - ethnic_group:lunch_type                 4     722.5 70035 3052.2
## - gender:is_first_child                   1      19.3 69331 3052.2
## - gender:lunch_type                       1      29.1 69341 3052.3
## - practice_sport:transport_means          2     265.1 69577 3052.3
## - gender:wkly_study_hours                 2     288.0 69600 3052.5
## - test_prep:is_first_child                1      76.6 69389 3052.7
## - test_prep:practice_sport                2     327.5 69640 3052.9
## - gender:practice_sport                   2     339.9 69652 3053.0
## - lunch_type:test_prep                    1     110.6 69423 3053.0
## - lunch_type:is_first_child               1     118.9 69431 3053.1
## - parent_educ:practice_sport             10    2314.2 71626 3053.5
## - ethnic_group:is_first_child             4     882.6 70195 3053.6
## - test_prep:transport_means               1     191.4 69503 3053.7
## <none>                                                69312 3054.1
## - is_first_child:transport_means          1     236.1 69548 3054.1
## - lunch_type:transport_means              1     283.0 69595 3054.5
## - practice_sport:wkly_study_hours         4    1043.8 70356 3054.9
## - parent_educ:is_first_child              5    1292.5 70605 3055.0
## - ethnic_group:transport_means            4    1109.2 70421 3055.5
## - parent_educ:parent_marital_status      15    3835.0 73147 3055.9
## - parent_marital_status:transport_means   3     935.7 70248 3056.0
## - test_prep:wkly_study_hours              2     703.5 70016 3056.1
## - lunch_type:wkly_study_hours             2     778.6 70091 3056.7
## + lunch_type:parent_marital_status        3     363.1 68949 3057.0
## + test_prep:parent_marital_status         2     100.8 69211 3057.2
## + ethnic_group:test_prep                  4     502.5 68810 3057.8
## + parent_educ:transport_means             5     651.6 68660 3058.5
## + parent_marital_status:practice_sport    5     507.8 68804 3059.8
## + gender:parent_marital_status            3      19.6 69293 3059.9
## + gender:parent_educ                      5     471.7 68840 3060.1
## + gender:ethnic_group                     4     167.2 69145 3060.7
## - lunch_type:practice_sport               2    1267.6 70580 3060.8
## + parent_educ:lunch_type                  5     356.7 68955 3061.0
## + ethnic_group:practice_sport             8    1016.1 68296 3061.4
## + parent_educ:wkly_study_hours           10    1340.9 67971 3062.6
## + ethnic_group:wkly_study_hours           8     789.2 68523 3063.3
## - parent_marital_status:wkly_study_hours  6    2550.9 71863 3063.4
## + parent_educ:test_prep                   5      50.5 69262 3063.7
## - parent_marital_status:is_first_child    3    2435.5 71748 3068.5
## + ethnic_group:parent_educ               20    2270.2 67042 3074.4
## 
## Step:  AIC=3050.96
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:parent_marital_status     11    2305.2 71719 3048.2
## - is_first_child:wkly_study_hours         2     191.9 69606 3048.6
## - transport_means:wkly_study_hours        2     205.6 69620 3048.7
## - practice_sport:transport_means          2     236.5 69651 3049.0
## - gender:transport_means                  1       2.8 69417 3049.0
## - gender:test_prep                        1       5.6 69420 3049.0
## - ethnic_group:lunch_type                 4     724.5 70139 3049.1
## - gender:is_first_child                   1      23.6 69438 3049.2
## - gender:lunch_type                       1      38.5 69453 3049.3
## - test_prep:is_first_child                1      52.7 69467 3049.4
## - gender:wkly_study_hours                 2     289.2 69703 3049.4
## - gender:practice_sport                   2     343.5 69758 3049.9
## - test_prep:practice_sport                2     349.8 69764 3049.9
## - parent_educ:practice_sport             10    2272.3 71686 3050.0
## - lunch_type:test_prep                    1     128.0 69542 3050.0
## - lunch_type:is_first_child               1     131.7 69546 3050.1
## - test_prep:transport_means               1     191.5 69606 3050.6
## - ethnic_group:is_first_child             4     907.0 70321 3050.6
## <none>                                                69414 3051.0
## - lunch_type:transport_means              1     270.0 69684 3051.2
## - is_first_child:transport_means          1     271.7 69686 3051.3
## - parent_educ:is_first_child              5    1261.5 70676 3051.6
## - ethnic_group:transport_means            4    1065.9 70480 3051.9
## - practice_sport:wkly_study_hours         4    1075.9 70490 3052.0
## - parent_educ:parent_marital_status      15    3782.3 73197 3052.3
## - parent_marital_status:transport_means   3     901.5 70316 3052.6
## - test_prep:wkly_study_hours              2     673.0 70087 3052.7
## - lunch_type:wkly_study_hours             2     782.5 70197 3053.6
## + practice_sport:is_first_child           2     102.1 69312 3054.1
## + lunch_type:parent_marital_status        3     336.6 69078 3054.1
## + test_prep:parent_marital_status         2      97.8 69316 3054.1
## + ethnic_group:test_prep                  4     524.0 68890 3054.5
## + parent_educ:transport_means             5     604.0 68810 3055.8
## + gender:parent_marital_status            3      18.0 69396 3056.8
## + gender:parent_educ                      5     484.2 68930 3056.8
## + parent_marital_status:practice_sport    5     446.7 68968 3057.2
## - lunch_type:practice_sport               2    1235.0 70649 3057.4
## + gender:ethnic_group                     4     187.0 69227 3057.4
## + parent_educ:lunch_type                  5     356.3 69058 3057.9
## + ethnic_group:practice_sport             8     949.0 68465 3058.8
## + parent_educ:wkly_study_hours           10    1293.2 68121 3059.9
## + ethnic_group:wkly_study_hours           8     799.5 68615 3060.1
## - parent_marital_status:wkly_study_hours  6    2548.9 71963 3060.2
## + parent_educ:test_prep                   5      54.2 69360 3060.5
## - parent_marital_status:is_first_child    3    2469.3 71884 3065.6
## + ethnic_group:parent_educ               20    2240.2 67174 3071.6
## 
## Step:  AIC=3048.23
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:practice_sport             10    1945.7 73665 3044.0
## - practice_sport:transport_means          2      95.5 71815 3045.0
## - ethnic_group:is_first_child             4     586.8 72306 3045.0
## - transport_means:wkly_study_hours        2     160.4 71880 3045.6
## - is_first_child:wkly_study_hours         2     167.1 71886 3045.6
## - gender:wkly_study_hours                 2     199.5 71919 3045.9
## - ethnic_group:lunch_type                 4     741.3 72461 3046.3
## - gender:transport_means                  1      24.5 71744 3046.4
## - gender:test_prep                        1      37.7 71757 3046.5
## - test_prep:is_first_child                1      40.0 71759 3046.6
## - gender:lunch_type                       1      42.6 71762 3046.6
## - gender:is_first_child                   1      52.0 71771 3046.7
## - test_prep:practice_sport                2     296.9 72016 3046.7
## - gender:practice_sport                   2     338.7 72058 3047.0
## - lunch_type:test_prep                    1      98.2 71818 3047.0
## - lunch_type:is_first_child               1      98.2 71818 3047.0
## - test_prep:transport_means               1     173.5 71893 3047.7
## - parent_educ:is_first_child              5    1201.7 72921 3048.0
## <none>                                                71719 3048.2
## - parent_marital_status:transport_means   3     741.3 72461 3048.3
## - practice_sport:wkly_study_hours         4     990.2 72710 3048.3
## - lunch_type:transport_means              1     320.0 72039 3048.9
## - is_first_child:transport_means          1     356.3 72076 3049.2
## - ethnic_group:transport_means            4    1128.0 72847 3049.4
## - lunch_type:wkly_study_hours             2     705.8 72425 3050.0
## - parent_educ:parent_marital_status      15    3998.6 75718 3050.2
## - test_prep:wkly_study_hours              2     820.6 72540 3050.9
## + ethnic_group:parent_marital_status     11    2305.2 69414 3051.0
## + ethnic_group:test_prep                  4     586.9 71132 3051.4
## + practice_sport:is_first_child           2      41.3 71678 3051.9
## - parent_marital_status:wkly_study_hours  6    1941.0 73660 3052.0
## + parent_educ:transport_means             5     747.1 70972 3052.1
## + lunch_type:parent_marital_status        3     219.1 71500 3052.4
## + test_prep:parent_marital_status         3     147.7 71572 3053.0
## + gender:parent_marital_status            3      84.7 71635 3053.5
## + gender:parent_educ                      5     442.4 71277 3054.6
## - lunch_type:practice_sport               2    1319.4 73039 3055.0
## + gender:ethnic_group                     4     146.6 71573 3055.0
## + parent_educ:lunch_type                  5     373.5 71346 3055.2
## + parent_marital_status:practice_sport    6     525.2 71194 3055.9
## + parent_educ:wkly_study_hours           10    1465.5 70254 3056.1
## + ethnic_group:practice_sport             8     879.1 70840 3057.0
## + parent_educ:test_prep                   5      50.8 71669 3057.8
## + ethnic_group:wkly_study_hours           8     747.7 70972 3058.1
## - parent_marital_status:is_first_child    3    2272.4 73992 3060.6
## + ethnic_group:parent_educ               20    2384.6 69335 3068.3
## 
## Step:  AIC=3044.03
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:is_first_child             4     616.0 74281 3040.9
## - practice_sport:transport_means          2     114.9 73780 3040.9
## - transport_means:wkly_study_hours        2     119.6 73785 3041.0
## - is_first_child:wkly_study_hours         2     175.7 73841 3041.4
## - ethnic_group:lunch_type                 4     736.1 74401 3041.9
## - gender:wkly_study_hours                 2     246.2 73911 3042.0
## - gender:lunch_type                       1      26.0 73691 3042.2
## - gender:practice_sport                   2     279.5 73945 3042.3
## - test_prep:is_first_child                1      51.2 73716 3042.4
## - gender:transport_means                  1      53.1 73718 3042.4
## - gender:test_prep                        1      56.7 73722 3042.5
## - gender:is_first_child                   1      66.4 73731 3042.6
## - lunch_type:is_first_child               1      79.2 73744 3042.7
## - test_prep:practice_sport                2     349.4 74014 3042.8
## - lunch_type:test_prep                    1     121.2 73786 3043.0
## - practice_sport:wkly_study_hours         4     879.5 74545 3043.0
## - test_prep:transport_means               1     145.6 73811 3043.2
## <none>                                                73665 3044.0
## - is_first_child:transport_means          1     260.1 73925 3044.1
## - lunch_type:transport_means              1     285.2 73950 3044.3
## - parent_educ:is_first_child              5    1425.4 75090 3045.3
## - ethnic_group:transport_means            4    1173.7 74839 3045.3
## - test_prep:wkly_study_hours              2     674.2 74339 3045.4
## - parent_marital_status:transport_means   3     930.7 74596 3045.4
## - lunch_type:wkly_study_hours             2     751.1 74416 3046.0
## + ethnic_group:test_prep                  4     596.7 73068 3047.2
## + practice_sport:is_first_child           2      23.4 73642 3047.8
## - parent_educ:parent_marital_status      15    4352.1 78017 3047.9
## - parent_marital_status:wkly_study_hours  6    2020.8 75686 3048.0
## + parent_educ:practice_sport             10    1945.7 71719 3048.2
## + lunch_type:parent_marital_status        3     173.9 73491 3048.6
## + test_prep:parent_marital_status         3     155.5 73510 3048.8
## - lunch_type:practice_sport               2    1103.6 74769 3048.8
## + parent_educ:transport_means             5     643.4 73022 3048.8
## + gender:parent_marital_status            3      77.3 73588 3049.4
## + ethnic_group:parent_marital_status     11    1978.6 71686 3050.0
## + gender:ethnic_group                     4     239.4 73426 3050.1
## + gender:parent_educ                      5     474.1 73191 3050.2
## + parent_educ:wkly_study_hours           10    1601.0 72064 3051.1
## + parent_educ:lunch_type                  5     343.0 73322 3051.3
## + parent_marital_status:practice_sport    6     420.8 73244 3052.6
## + ethnic_group:practice_sport             8     895.6 72769 3052.8
## + parent_educ:test_prep                   5      96.6 73568 3053.2
## + ethnic_group:wkly_study_hours           8     768.5 72897 3053.8
## - parent_marital_status:is_first_child    3    2307.1 75972 3056.2
## + ethnic_group:parent_educ               20    2365.9 71299 3064.8
## 
## Step:  AIC=3040.94
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:lunch_type                 4     559.7 74841 3037.4
## - practice_sport:transport_means          2     104.8 74386 3037.8
## - transport_means:wkly_study_hours        2     126.4 74407 3037.9
## - gender:wkly_study_hours                 2     196.4 74477 3038.5
## - is_first_child:wkly_study_hours         2     229.6 74511 3038.8
## - gender:practice_sport                   2     251.9 74533 3038.9
## - gender:lunch_type                       1      14.3 74295 3039.1
## - gender:is_first_child                   1      30.8 74312 3039.2
## - gender:test_prep                        1      40.0 74321 3039.3
## - gender:transport_means                  1      58.5 74340 3039.4
## - test_prep:is_first_child                1      75.8 74357 3039.5
## - test_prep:practice_sport                2     350.0 74631 3039.7
## - test_prep:transport_means               1     115.1 74396 3039.8
## - lunch_type:is_first_child               1     119.2 74400 3039.9
## - practice_sport:wkly_study_hours         4     880.0 75161 3039.9
## - is_first_child:transport_means          1     144.6 74426 3040.1
## - lunch_type:test_prep                    1     149.4 74430 3040.1
## <none>                                                74281 3040.9
## - lunch_type:transport_means              1     261.8 74543 3041.0
## - test_prep:wkly_study_hours              2     522.3 74803 3041.1
## - parent_marital_status:transport_means   3     939.6 75221 3042.3
## - lunch_type:wkly_study_hours             2     692.9 74974 3042.4
## - parent_educ:is_first_child              5    1465.0 75746 3042.5
## - ethnic_group:transport_means            4    1307.4 75588 3043.2
## - parent_educ:parent_marital_status      15    4239.6 78521 3043.7
## + ethnic_group:is_first_child             4     616.0 73665 3044.0
## + ethnic_group:test_prep                  4     581.5 73700 3044.3
## - parent_marital_status:wkly_study_hours  6    1978.0 76259 3044.4
## + practice_sport:is_first_child           2      40.8 74240 3044.6
## + parent_educ:practice_sport             10    1974.9 72306 3045.0
## + test_prep:parent_marital_status         3     184.2 74097 3045.5
## - lunch_type:practice_sport               2    1103.4 75384 3045.6
## + lunch_type:parent_marital_status        3     140.1 74141 3045.8
## + parent_educ:transport_means             5     610.0 73671 3046.1
## + gender:parent_marital_status            3      67.0 74214 3046.4
## + gender:ethnic_group                     4     192.3 74089 3047.4
## + gender:parent_educ                      5     422.0 73859 3047.6
## + parent_educ:wkly_study_hours           10    1654.5 72627 3047.7
## + parent_educ:lunch_type                  5     349.3 73932 3048.2
## + ethnic_group:parent_marital_status     11    1673.1 72608 3049.5
## + parent_marital_status:practice_sport    6     385.1 73896 3049.9
## + parent_educ:test_prep                   5     113.8 74167 3050.0
## + ethnic_group:practice_sport             8     857.0 73424 3050.1
## + ethnic_group:wkly_study_hours           8     741.7 73539 3051.0
## - parent_marital_status:is_first_child    3    2299.8 76581 3052.9
## + ethnic_group:parent_educ               20    2402.3 71879 3061.5
## 
## Step:  AIC=3037.37
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - practice_sport:transport_means          2      90.2 74931 3034.1
## - transport_means:wkly_study_hours        2     140.4 74981 3034.5
## - gender:wkly_study_hours                 2     204.9 75046 3035.0
## - gender:practice_sport                   2     215.5 75056 3035.1
## - is_first_child:wkly_study_hours         2     223.2 75064 3035.1
## - gender:lunch_type                       1      15.2 74856 3035.5
## - practice_sport:wkly_study_hours         4     784.5 75625 3035.5
## - gender:is_first_child                   1      33.8 74875 3035.6
## - gender:test_prep                        1      48.7 74889 3035.8
## - gender:transport_means                  1      52.5 74893 3035.8
## - test_prep:is_first_child                1      66.9 74908 3035.9
## - lunch_type:is_first_child               1     106.1 74947 3036.2
## - test_prep:transport_means               1     128.1 74969 3036.4
## - is_first_child:transport_means          1     137.8 74979 3036.4
## - test_prep:practice_sport                2     407.4 75248 3036.6
## - lunch_type:test_prep                    1     182.2 75023 3036.8
## <none>                                                74841 3037.4
## - test_prep:wkly_study_hours              2     520.3 75361 3037.5
## - lunch_type:transport_means              1     325.7 75166 3037.9
## - parent_educ:parent_marital_status      15    4029.3 78870 3038.3
## - lunch_type:wkly_study_hours             2     641.3 75482 3038.4
## - parent_marital_status:transport_means   3     902.6 75743 3038.4
## - ethnic_group:transport_means            4    1226.6 76067 3039.0
## - parent_educ:is_first_child              5    1535.8 76377 3039.3
## + ethnic_group:lunch_type                 4     559.7 74281 3040.9
## + practice_sport:is_first_child           2      47.5 74793 3041.0
## - parent_marital_status:wkly_study_hours  6    2059.5 76900 3041.4
## + ethnic_group:test_prep                  4     468.2 74373 3041.7
## + parent_educ:practice_sport             10    1964.0 72877 3041.7
## + test_prep:parent_marital_status         3     192.8 74648 3041.8
## + ethnic_group:is_first_child             4     439.7 74401 3041.9
## + parent_educ:transport_means             5     683.2 74158 3042.0
## + lunch_type:parent_marital_status        3     164.7 74676 3042.1
## + gender:parent_marital_status            3      61.4 74779 3042.9
## - lunch_type:practice_sport               2    1228.5 76069 3043.0
## + gender:ethnic_group                     4     211.7 74629 3043.7
## + parent_educ:lunch_type                  5     391.3 74449 3044.3
## + gender:parent_educ                      5     376.2 74465 3044.4
## + parent_marital_status:practice_sport    6     466.6 74374 3045.7
## + ethnic_group:practice_sport             8     965.1 73876 3045.7
## + ethnic_group:parent_marital_status     11    1696.6 73144 3045.8
## + parent_educ:wkly_study_hours           10    1444.5 73396 3045.9
## + parent_educ:test_prep                   5     122.2 74719 3046.4
## + ethnic_group:wkly_study_hours           8     794.9 74046 3047.1
## - parent_marital_status:is_first_child    3    2267.8 77109 3049.0
## + ethnic_group:parent_educ               20    2517.8 72323 3057.2
## 
## Step:  AIC=3034.08
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - transport_means:wkly_study_hours        2     152.6 75084 3031.3
## - gender:practice_sport                   2     202.8 75134 3031.7
## - gender:wkly_study_hours                 2     209.1 75140 3031.7
## - is_first_child:wkly_study_hours         2     215.6 75147 3031.8
## - practice_sport:wkly_study_hours         4     763.7 75695 3032.1
## - gender:lunch_type                       1      15.9 74947 3032.2
## - gender:is_first_child                   1      39.1 74970 3032.4
## - gender:test_prep                        1      46.4 74977 3032.4
## - gender:transport_means                  1      52.6 74984 3032.5
## - test_prep:is_first_child                1      65.8 74997 3032.6
## - lunch_type:is_first_child               1     113.8 75045 3033.0
## - test_prep:transport_means               1     124.1 75055 3033.1
## - test_prep:practice_sport                2     399.1 75330 3033.2
## - is_first_child:transport_means          1     157.6 75089 3033.3
## - lunch_type:test_prep                    1     200.4 75131 3033.7
## <none>                                                74931 3034.1
## - test_prep:wkly_study_hours              2     521.1 75452 3034.2
## - lunch_type:transport_means              1     334.9 75266 3034.7
## - parent_educ:parent_marital_status      15    4028.6 78960 3035.0
## - lunch_type:wkly_study_hours             2     635.2 75566 3035.1
## - parent_marital_status:transport_means   3     917.6 75849 3035.3
## - ethnic_group:transport_means            4    1237.8 76169 3035.8
## - parent_educ:is_first_child              5    1530.9 76462 3036.0
## + practice_sport:transport_means          2      90.2 74841 3037.4
## + ethnic_group:lunch_type                 4     545.2 74386 3037.8
## + practice_sport:is_first_child           2      36.5 74894 3037.8
## - parent_marital_status:wkly_study_hours  6    2071.5 77003 3038.2
## + parent_educ:practice_sport             10    1980.6 72950 3038.3
## + ethnic_group:test_prep                  4     468.3 74463 3038.4
## + test_prep:parent_marital_status         3     193.8 74737 3038.6
## + ethnic_group:is_first_child             4     436.2 74495 3038.6
## + lunch_type:parent_marital_status        3     164.8 74766 3038.8
## + parent_educ:transport_means             5     623.6 74307 3039.2
## - lunch_type:practice_sport               2    1207.3 76138 3039.5
## + gender:parent_marital_status            3      49.0 74882 3039.7
## + gender:ethnic_group                     4     211.2 74720 3040.4
## + parent_educ:lunch_type                  5     407.0 74524 3040.9
## + gender:parent_educ                      5     361.2 74570 3041.2
## + parent_marital_status:practice_sport    6     464.0 74467 3042.4
## + ethnic_group:practice_sport             8     951.2 73980 3042.5
## + parent_educ:test_prep                   5     126.5 74805 3043.1
## + ethnic_group:parent_marital_status     11    1608.8 73322 3043.3
## + parent_educ:wkly_study_hours           10    1355.5 73576 3043.3
## + ethnic_group:wkly_study_hours           8     794.8 74136 3043.8
## - parent_marital_status:is_first_child    3    2227.1 77158 3045.4
## + ethnic_group:parent_educ               20    2387.1 72544 3055.0
## 
## Step:  AIC=3031.28
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:wkly_study_hours                 2     200.3 75284 3028.8
## - gender:practice_sport                   2     213.6 75297 3029.0
## - is_first_child:wkly_study_hours         2     235.6 75319 3029.1
## - practice_sport:wkly_study_hours         4     769.9 75854 3029.3
## - gender:lunch_type                       1      13.4 75097 3029.4
## - gender:is_first_child                   1      36.5 75120 3029.6
## - gender:test_prep                        1      36.9 75121 3029.6
## - gender:transport_means                  1      52.0 75136 3029.7
## - test_prep:is_first_child                1      73.0 75157 3029.8
## - test_prep:transport_means               1     106.3 75190 3030.1
## - lunch_type:is_first_child               1     117.0 75201 3030.2
## - is_first_child:transport_means          1     155.5 75239 3030.5
## - test_prep:practice_sport                2     432.0 75516 3030.7
## - lunch_type:test_prep                    1     202.7 75286 3030.9
## - test_prep:wkly_study_hours              2     502.3 75586 3031.2
## <none>                                                75084 3031.3
## - lunch_type:transport_means              1     316.8 75400 3031.8
## - parent_educ:parent_marital_status      15    4009.8 79093 3032.0
## - parent_marital_status:transport_means   3     899.1 75983 3032.3
## - lunch_type:wkly_study_hours             2     642.7 75726 3032.3
## - parent_educ:is_first_child              5    1516.3 76600 3033.1
## - ethnic_group:transport_means            4    1313.2 76397 3033.5
## + transport_means:wkly_study_hours        2     152.6 74931 3034.1
## + practice_sport:transport_means          2     102.4 74981 3034.5
## + ethnic_group:lunch_type                 4     557.6 74526 3034.9
## + practice_sport:is_first_child           2      38.3 75045 3035.0
## + ethnic_group:test_prep                  4     478.7 74605 3035.5
## - parent_marital_status:wkly_study_hours  6    2093.8 77177 3035.5
## + test_prep:parent_marital_status         3     190.2 74893 3035.8
## + ethnic_group:is_first_child             4     437.3 74646 3035.8
## + parent_educ:practice_sport             10    1938.5 73145 3035.8
## + lunch_type:parent_marital_status        3     176.1 74908 3035.9
## + parent_educ:transport_means             5     615.5 74468 3036.4
## - lunch_type:practice_sport               2    1206.4 76290 3036.7
## + gender:parent_marital_status            3      42.7 75041 3036.9
## + gender:ethnic_group                     4     235.5 74848 3037.4
## + parent_educ:lunch_type                  5     412.6 74671 3038.0
## + gender:parent_educ                      5     381.1 74703 3038.3
## + ethnic_group:practice_sport             8     981.1 74103 3039.5
## + parent_marital_status:practice_sport    6     470.9 74613 3039.6
## + parent_educ:test_prep                   5     132.3 74951 3040.2
## + parent_educ:wkly_study_hours           10    1382.8 73701 3040.3
## + ethnic_group:parent_marital_status     11    1599.1 73485 3040.6
## + ethnic_group:wkly_study_hours           8     685.4 74398 3041.9
## - parent_marital_status:is_first_child    3    2151.3 77235 3041.9
## + ethnic_group:parent_educ               20    2409.9 72674 3052.0
## 
## Step:  AIC=3028.85
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - is_first_child:wkly_study_hours         2     224.7 75509 3026.6
## - gender:practice_sport                   2     227.7 75512 3026.6
## - practice_sport:wkly_study_hours         4     746.4 76030 3026.7
## - gender:lunch_type                       1       9.6 75293 3026.9
## - gender:is_first_child                   1      35.4 75319 3027.1
## - gender:test_prep                        1      54.5 75338 3027.3
## - gender:transport_means                  1      55.2 75339 3027.3
## - test_prep:is_first_child                1      91.8 75376 3027.6
## - lunch_type:is_first_child               1     110.5 75394 3027.7
## - test_prep:transport_means               1     115.1 75399 3027.8
## - is_first_child:transport_means          1     143.5 75427 3028.0
## - test_prep:practice_sport                2     412.6 75696 3028.1
## - lunch_type:test_prep                    1     200.7 75485 3028.4
## - test_prep:wkly_study_hours              2     501.3 75785 3028.8
## <none>                                                75284 3028.8
## - lunch_type:transport_means              1     311.9 75596 3029.3
## - lunch_type:wkly_study_hours             2     588.5 75872 3029.4
## - parent_educ:parent_marital_status      15    4077.9 79362 3030.0
## - parent_marital_status:transport_means   3     918.3 76202 3030.0
## - parent_educ:is_first_child              5    1504.4 76788 3030.5
## - ethnic_group:transport_means            4    1307.8 76592 3031.0
## + gender:wkly_study_hours                 2     200.3 75084 3031.3
## + transport_means:wkly_study_hours        2     143.7 75140 3031.7
## + practice_sport:transport_means          2     106.7 75177 3032.0
## + ethnic_group:lunch_type                 4     564.3 74720 3032.4
## + practice_sport:is_first_child           2      35.0 75249 3032.6
## + ethnic_group:test_prep                  4     500.5 74783 3032.9
## + parent_educ:practice_sport             10    1975.2 73309 3033.2
## + test_prep:parent_marital_status         3     190.2 75094 3033.4
## + lunch_type:parent_marital_status        3     151.8 75132 3033.7
## + ethnic_group:is_first_child             4     393.3 74891 3033.8
## - lunch_type:practice_sport               2    1171.7 76456 3034.0
## + parent_educ:transport_means             5     584.3 74700 3034.2
## + gender:parent_marital_status            3      40.2 75244 3034.5
## - parent_marital_status:wkly_study_hours  6    2307.6 77592 3034.7
## + gender:ethnic_group                     4     245.5 75038 3034.9
## + gender:parent_educ                      5     409.5 74874 3035.6
## + parent_educ:lunch_type                  5     400.9 74883 3035.7
## + ethnic_group:practice_sport             8    1028.4 74255 3036.7
## + parent_marital_status:practice_sport    6     482.3 74802 3037.1
## + parent_educ:wkly_study_hours           10    1462.3 73822 3037.3
## + parent_educ:test_prep                   5     144.3 75140 3037.7
## + ethnic_group:parent_marital_status     11    1560.9 73723 3038.5
## - parent_marital_status:is_first_child    3    2096.8 77381 3039.1
## + ethnic_group:wkly_study_hours           8     665.0 74619 3039.6
## + ethnic_group:parent_educ               20    2348.0 72936 3050.2
## 
## Step:  AIC=3026.61
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:practice_sport                   2     221.8 75730 3024.3
## - gender:lunch_type                       1       8.1 75517 3024.7
## - practice_sport:wkly_study_hours         4     815.9 76325 3024.9
## - gender:is_first_child                   1      47.0 75556 3025.0
## - gender:test_prep                        1      56.0 75565 3025.1
## - gender:transport_means                  1      60.8 75569 3025.1
## - test_prep:is_first_child                1      66.3 75575 3025.1
## - is_first_child:transport_means          1     121.9 75631 3025.6
## - test_prep:practice_sport                2     387.2 75896 3025.6
## - test_prep:transport_means               1     132.1 75641 3025.6
## - lunch_type:is_first_child               1     147.3 75656 3025.8
## - lunch_type:test_prep                    1     226.8 75735 3026.4
## - test_prep:wkly_study_hours              2     504.9 76014 3026.5
## <none>                                                75509 3026.6
## - lunch_type:transport_means              1     315.6 75824 3027.1
## - parent_marital_status:transport_means   3     854.9 76364 3027.2
## - lunch_type:wkly_study_hours             2     599.4 76108 3027.3
## - parent_educ:is_first_child              5    1416.9 76926 3027.6
## - parent_educ:parent_marital_status      15    4118.0 79627 3027.9
## - ethnic_group:transport_means            4    1292.0 76801 3028.6
## + is_first_child:wkly_study_hours         2     224.7 75284 3028.8
## + gender:wkly_study_hours                 2     189.4 75319 3029.1
## + transport_means:wkly_study_hours        2     162.2 75346 3029.3
## + practice_sport:transport_means          2      99.0 75410 3029.8
## + ethnic_group:lunch_type                 4     561.9 74947 3030.2
## + practice_sport:is_first_child           2      29.1 75480 3030.4
## + ethnic_group:test_prep                  4     516.9 74992 3030.6
## + test_prep:parent_marital_status         3     216.2 75292 3030.9
## + parent_educ:practice_sport             10    1970.1 73539 3031.0
## + ethnic_group:is_first_child             4     436.1 75073 3031.2
## + lunch_type:parent_marital_status        3     148.9 75360 3031.4
## + parent_educ:transport_means             5     557.1 74952 3032.2
## + gender:parent_marital_status            3      43.2 75466 3032.3
## + gender:ethnic_group                     4     258.6 75250 3032.6
## - lunch_type:practice_sport               2    1314.3 76823 3032.8
## - parent_marital_status:wkly_study_hours  6    2397.4 77906 3033.1
## + gender:parent_educ                      5     449.5 75059 3033.1
## + parent_educ:lunch_type                  5     402.2 75106 3033.5
## + ethnic_group:practice_sport             8    1054.8 74454 3034.3
## + parent_marital_status:practice_sport    6     535.4 74973 3034.4
## + parent_educ:wkly_study_hours           10    1496.8 74012 3034.8
## + parent_educ:test_prep                   5     130.5 75378 3035.6
## - parent_marital_status:is_first_child    3    2033.1 77542 3036.3
## + ethnic_group:parent_marital_status     11    1481.0 74028 3036.9
## + ethnic_group:wkly_study_hours           8     699.9 74809 3037.1
## + ethnic_group:parent_educ               20    2251.9 73257 3048.8
## 
## Step:  AIC=3024.34
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:is_first_child + gender:transport_means + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:lunch_type                       1       8.4 75739 3022.4
## - test_prep:is_first_child                1      55.9 75786 3022.8
## - gender:is_first_child                   1      57.4 75788 3022.8
## - gender:transport_means                  1      71.5 75802 3022.9
## - gender:test_prep                        1      71.6 75802 3022.9
## - practice_sport:wkly_study_hours         4     886.4 76617 3023.2
## - test_prep:transport_means               1     123.7 75854 3023.3
## - is_first_child:transport_means          1     137.4 75868 3023.4
## - test_prep:practice_sport                2     423.8 76154 3023.6
## - lunch_type:is_first_child               1     180.2 75911 3023.7
## - lunch_type:test_prep                    1     217.8 75948 3024.0
## - test_prep:wkly_study_hours              2     495.1 76226 3024.2
## <none>                                                75730 3024.3
## - parent_marital_status:transport_means   3     814.9 76545 3024.7
## - lunch_type:wkly_study_hours             2     575.3 76306 3024.8
## - lunch_type:transport_means              1     337.3 76068 3025.0
## - parent_educ:is_first_child              5    1435.2 77166 3025.4
## - parent_educ:parent_marital_status      15    4197.3 79928 3026.2
## - ethnic_group:transport_means            4    1300.0 77030 3026.4
## + gender:practice_sport                   2     221.8 75509 3026.6
## + is_first_child:wkly_study_hours         2     218.8 75512 3026.6
## + gender:wkly_study_hours                 2     202.8 75528 3026.8
## + transport_means:wkly_study_hours        2     172.4 75558 3027.0
## + practice_sport:transport_means          2      85.5 75645 3027.7
## + practice_sport:is_first_child           2      28.3 75702 3028.1
## + ethnic_group:lunch_type                 4     527.5 75203 3028.2
## + ethnic_group:test_prep                  4     516.9 75214 3028.3
## + test_prep:parent_marital_status         3     200.8 75530 3028.8
## + ethnic_group:is_first_child             4     413.3 75317 3029.1
## + parent_educ:practice_sport             10    1917.0 73813 3029.2
## + lunch_type:parent_marital_status        3     137.0 75593 3029.3
## + parent_educ:transport_means             5     565.9 75165 3029.9
## + gender:parent_marital_status            3      52.3 75678 3029.9
## - parent_marital_status:wkly_study_hours  6    2321.3 78052 3030.2
## + gender:ethnic_group                     4     216.3 75514 3030.7
## - lunch_type:practice_sport               2    1351.3 77082 3030.8
## + gender:parent_educ                      5     453.1 75277 3030.8
## + parent_educ:lunch_type                  5     416.7 75314 3031.1
## + ethnic_group:practice_sport             8    1124.5 74606 3031.5
## + parent_marital_status:practice_sport    6     558.5 75172 3032.0
## + parent_educ:wkly_study_hours           10    1460.2 74270 3032.8
## + parent_educ:test_prep                   5     130.2 75600 3033.3
## - parent_marital_status:is_first_child    3    2060.2 77791 3034.2
## + ethnic_group:parent_marital_status     11    1515.3 74215 3034.4
## + ethnic_group:wkly_study_hours           8     702.9 75028 3034.8
## + ethnic_group:parent_educ               20    2304.5 73426 3046.1
## 
## Step:  AIC=3022.41
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:test_prep + gender:is_first_child + 
##     gender:transport_means + ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:is_first_child                   1      57.0 75796 3020.8
## - test_prep:is_first_child                1      57.1 75796 3020.8
## - gender:test_prep                        1      69.1 75808 3020.9
## - gender:transport_means                  1      72.9 75812 3021.0
## - practice_sport:wkly_study_hours         4     884.1 76623 3021.2
## - test_prep:transport_means               1     127.3 75866 3021.4
## - is_first_child:transport_means          1     134.3 75873 3021.4
## - test_prep:practice_sport                2     429.7 76169 3021.7
## - lunch_type:is_first_child               1     182.4 75921 3021.8
## - lunch_type:test_prep                    1     226.2 75965 3022.2
## - test_prep:wkly_study_hours              2     500.1 76239 3022.3
## <none>                                                75739 3022.4
## - parent_marital_status:transport_means   3     808.4 76547 3022.7
## - lunch_type:wkly_study_hours             2     572.3 76311 3022.8
## - lunch_type:transport_means              1     345.8 76085 3023.1
## - parent_educ:is_first_child              5    1434.6 77173 3023.5
## - parent_educ:parent_marital_status      15    4194.5 79933 3024.2
## + gender:lunch_type                       1       8.4 75730 3024.3
## - ethnic_group:transport_means            4    1313.0 77052 3024.6
## + gender:practice_sport                   2     222.1 75517 3024.7
## + is_first_child:wkly_study_hours         2     217.1 75522 3024.7
## + gender:wkly_study_hours                 2     199.5 75539 3024.8
## + transport_means:wkly_study_hours        2     170.3 75569 3025.1
## + practice_sport:transport_means          2      85.8 75653 3025.7
## + practice_sport:is_first_child           2      28.3 75711 3026.2
## + ethnic_group:lunch_type                 4     527.2 75212 3026.3
## + ethnic_group:test_prep                  4     519.0 75220 3026.3
## + test_prep:parent_marital_status         3     203.5 75535 3026.8
## + ethnic_group:is_first_child             4     409.1 75330 3027.2
## + lunch_type:parent_marital_status        3     142.1 75597 3027.3
## + parent_educ:practice_sport             10    1903.8 73835 3027.4
## + parent_educ:transport_means             5     572.4 75166 3027.9
## + gender:parent_marital_status            3      51.1 75688 3028.0
## - parent_marital_status:wkly_study_hours  6    2359.0 78098 3028.5
## + gender:ethnic_group                     4     216.1 75523 3028.7
## + gender:parent_educ                      5     450.2 75289 3028.9
## + parent_educ:lunch_type                  5     424.1 75315 3029.1
## - lunch_type:practice_sport               2    1386.6 77125 3029.1
## + ethnic_group:practice_sport             8    1102.7 74636 3029.8
## + parent_marital_status:practice_sport    6     554.6 75184 3030.1
## + parent_educ:wkly_study_hours           10    1456.2 74283 3030.9
## + parent_educ:test_prep                   5     128.7 75610 3031.4
## - parent_marital_status:is_first_child    3    2051.8 77791 3032.2
## + ethnic_group:parent_marital_status     11    1513.5 74225 3032.5
## + ethnic_group:wkly_study_hours           8     705.0 75034 3032.9
## + ethnic_group:parent_educ               20    2265.2 73474 3044.5
## 
## Step:  AIC=3020.85
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:test_prep + gender:transport_means + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:test_prep                        1      63.1 75859 3019.3
## - test_prep:is_first_child                1      65.8 75862 3019.4
## - gender:transport_means                  1      71.8 75868 3019.4
## - is_first_child:transport_means          1     124.6 75921 3019.8
## - test_prep:transport_means               1     129.3 75925 3019.8
## - practice_sport:wkly_study_hours         4     920.1 76716 3020.0
## - test_prep:practice_sport                2     414.2 76210 3020.1
## - lunch_type:is_first_child               1     171.5 75967 3020.2
## - test_prep:wkly_study_hours              2     490.6 76286 3020.7
## - lunch_type:test_prep                    1     235.7 76032 3020.7
## <none>                                                75796 3020.8
## - lunch_type:wkly_study_hours             2     573.9 76370 3021.3
## - parent_marital_status:transport_means   3     837.6 76634 3021.3
## - lunch_type:transport_means              1     365.6 76161 3021.7
## - parent_educ:is_first_child              5    1471.7 77268 3022.2
## + gender:is_first_child                   1      57.0 75739 3022.4
## - parent_educ:parent_marital_status      15    4190.6 79986 3022.6
## + gender:lunch_type                       1       8.1 75788 3022.8
## + gender:practice_sport                   2     232.2 75564 3023.0
## + is_first_child:wkly_study_hours         2     230.4 75565 3023.1
## + gender:wkly_study_hours                 2     198.3 75598 3023.3
## - ethnic_group:transport_means            4    1355.1 77151 3023.3
## + transport_means:wkly_study_hours        2     165.8 75630 3023.6
## + practice_sport:transport_means          2      91.4 75704 3024.1
## + practice_sport:is_first_child           2      30.8 75765 3024.6
## + ethnic_group:lunch_type                 4     528.1 75268 3024.7
## + ethnic_group:test_prep                  4     488.7 75307 3025.0
## + test_prep:parent_marital_status         3     207.7 75588 3025.2
## + lunch_type:parent_marital_status        3     150.2 75646 3025.7
## + parent_educ:practice_sport             10    1908.4 73887 3025.8
## + ethnic_group:is_first_child             4     370.0 75426 3026.0
## + gender:parent_marital_status            3      58.6 75737 3026.4
## + parent_educ:transport_means             5     568.5 75227 3026.4
## - parent_marital_status:wkly_study_hours  6    2312.6 78108 3026.6
## + gender:ethnic_group                     4     219.5 75576 3027.1
## + parent_educ:lunch_type                  5     453.2 75343 3027.3
## + gender:parent_educ                      5     447.8 75348 3027.3
## - lunch_type:practice_sport               2    1433.9 77230 3027.9
## + ethnic_group:practice_sport             8    1075.1 74721 3028.4
## + parent_marital_status:practice_sport    6     536.8 75259 3028.7
## + parent_educ:wkly_study_hours           10    1464.0 74332 3029.3
## + parent_educ:test_prep                   5     129.7 75666 3029.8
## - parent_marital_status:is_first_child    3    2041.9 77838 3030.5
## + ethnic_group:parent_marital_status     11    1532.8 74263 3030.8
## + ethnic_group:wkly_study_hours           8     698.7 75097 3031.4
## + ethnic_group:parent_educ               20    2190.8 73605 3043.5
## 
## Step:  AIC=3019.34
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:transport_means + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:transport_means                  1      61.1 75920 3017.8
## - test_prep:is_first_child                1      66.6 75926 3017.9
## - is_first_child:transport_means          1     121.1 75980 3018.3
## - test_prep:transport_means               1     123.3 75982 3018.3
## - practice_sport:wkly_study_hours         4     907.1 76766 3018.3
## - test_prep:practice_sport                2     408.5 76267 3018.5
## - lunch_type:is_first_child               1     162.8 76022 3018.6
## - test_prep:wkly_study_hours              2     472.7 76332 3019.0
## - lunch_type:test_prep                    1     249.1 76108 3019.3
## <none>                                                75859 3019.3
## - lunch_type:wkly_study_hours             2     582.1 76441 3019.8
## - parent_marital_status:transport_means   3     852.8 76712 3019.9
## - lunch_type:transport_means              1     379.7 76239 3020.3
## - parent_educ:is_first_child              5    1449.5 77308 3020.5
## - parent_educ:parent_marital_status      15    4159.3 80018 3020.8
## + gender:test_prep                        1      63.1 75796 3020.8
## + gender:is_first_child                   1      51.0 75808 3020.9
## + gender:lunch_type                       1       5.8 75853 3021.3
## + gender:practice_sport                   2     246.4 75613 3021.4
## + is_first_child:wkly_study_hours         2     231.2 75628 3021.5
## + gender:wkly_study_hours                 2     218.9 75640 3021.6
## - ethnic_group:transport_means            4    1372.6 77232 3021.9
## + transport_means:wkly_study_hours        2     153.6 75705 3022.1
## + practice_sport:transport_means          2      88.4 75771 3022.7
## + practice_sport:is_first_child           2      33.0 75826 3023.1
## + ethnic_group:lunch_type                 4     538.8 75320 3023.1
## + ethnic_group:test_prep                  4     464.8 75394 3023.7
## + test_prep:parent_marital_status         3     205.5 75653 3023.7
## + lunch_type:parent_marital_status        3     157.5 75702 3024.1
## + parent_educ:practice_sport             10    1925.9 73933 3024.2
## + ethnic_group:is_first_child             4     351.2 75508 3024.6
## - parent_marital_status:wkly_study_hours  6    2281.3 78140 3024.8
## + gender:parent_marital_status            3      61.3 75798 3024.9
## + parent_educ:transport_means             5     558.7 75300 3025.0
## + gender:ethnic_group                     4     231.9 75627 3025.5
## + gender:parent_educ                      5     446.9 75412 3025.8
## + parent_educ:lunch_type                  5     444.2 75415 3025.9
## - lunch_type:practice_sport               2    1417.7 77277 3026.3
## + parent_marital_status:practice_sport    6     550.5 75308 3027.0
## + ethnic_group:practice_sport             8    1054.5 74804 3027.1
## + parent_educ:wkly_study_hours           10    1478.9 74380 3027.7
## + parent_educ:test_prep                   5     132.2 75727 3028.3
## - parent_marital_status:is_first_child    3    2002.0 77861 3028.7
## + ethnic_group:parent_marital_status     11    1567.5 74291 3029.0
## + ethnic_group:wkly_study_hours           8     725.0 75134 3029.7
## + ethnic_group:parent_educ               20    2197.5 73662 3042.0
## 
## Step:  AIC=3017.81
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:is_first_child                1      71.6 75992 3016.4
## - practice_sport:wkly_study_hours         4     888.2 76808 3016.7
## - is_first_child:transport_means          1     131.9 76052 3016.8
## - test_prep:transport_means               1     138.8 76059 3016.9
## - test_prep:practice_sport                2     403.4 76323 3016.9
## - lunch_type:is_first_child               1     150.7 76071 3017.0
## - test_prep:wkly_study_hours              2     477.5 76397 3017.5
## - lunch_type:test_prep                    1     253.8 76174 3017.8
## <none>                                                75920 3017.8
## - lunch_type:wkly_study_hours             2     565.9 76486 3018.2
## - parent_marital_status:transport_means   3     851.0 76771 3018.4
## - parent_educ:is_first_child              5    1432.0 77352 3018.8
## - lunch_type:transport_means              1     393.6 76314 3018.9
## - parent_educ:parent_marital_status      15    4127.3 80047 3019.1
## + gender:transport_means                  1      61.1 75859 3019.3
## + gender:test_prep                        1      52.4 75868 3019.4
## + gender:is_first_child                   1      50.5 75870 3019.4
## + gender:lunch_type                       1       7.1 75913 3019.8
## + gender:practice_sport                   2     255.3 75665 3019.8
## + is_first_child:wkly_study_hours         2     236.9 75683 3020.0
## + gender:wkly_study_hours                 2     221.6 75698 3020.1
## - ethnic_group:transport_means            4    1335.2 77255 3020.1
## + transport_means:wkly_study_hours        2     154.0 75766 3020.6
## + practice_sport:transport_means          2      89.3 75831 3021.1
## + practice_sport:is_first_child           2      37.7 75882 3021.5
## + ethnic_group:lunch_type                 4     532.3 75388 3021.7
## + ethnic_group:test_prep                  4     467.3 75453 3022.2
## + test_prep:parent_marital_status         3     200.6 75719 3022.2
## + parent_educ:practice_sport             10    1954.7 73965 3022.4
## + lunch_type:parent_marital_status        3     160.5 75760 3022.6
## + ethnic_group:is_first_child             4     355.2 75565 3023.1
## - parent_marital_status:wkly_study_hours  6    2270.6 78191 3023.2
## + gender:parent_marital_status            3      59.3 75861 3023.3
## + parent_educ:transport_means             5     560.2 75360 3023.4
## + gender:ethnic_group                     4     247.9 75672 3023.9
## + gender:parent_educ                      5     449.9 75470 3024.3
## + parent_educ:lunch_type                  5     448.9 75471 3024.3
## - lunch_type:practice_sport               2    1396.7 77317 3024.6
## + parent_marital_status:practice_sport    6     550.3 75370 3025.5
## + ethnic_group:practice_sport             8    1036.1 74884 3025.7
## + parent_educ:wkly_study_hours           10    1435.0 74485 3026.6
## + parent_educ:test_prep                   5     128.0 75792 3026.8
## + ethnic_group:parent_marital_status     11    1602.7 74317 3027.2
## - parent_marital_status:is_first_child    3    2036.3 77956 3027.4
## + ethnic_group:wkly_study_hours           8     718.1 75202 3028.2
## + ethnic_group:parent_educ               20    2173.1 73747 3040.7
## - gender                                  1   12750.1 88670 3107.4
## 
## Step:  AIC=3016.37
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:practice_sport + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - practice_sport:wkly_study_hours         4     915.5 76907 3015.4
## - is_first_child:transport_means          1     140.3 76132 3015.5
## - test_prep:transport_means               1     140.4 76132 3015.5
## - test_prep:practice_sport                2     403.2 76395 3015.5
## - lunch_type:is_first_child               1     166.0 76158 3015.7
## - test_prep:wkly_study_hours              2     471.7 76463 3016.0
## - lunch_type:test_prep                    1     244.8 76236 3016.3
## <none>                                                75992 3016.4
## - parent_marital_status:transport_means   3     837.7 76829 3016.8
## - lunch_type:wkly_study_hours             2     582.5 76574 3016.9
## - parent_educ:is_first_child              5    1386.8 77378 3017.0
## - parent_educ:parent_marital_status      15    4132.9 80125 3017.6
## - lunch_type:transport_means              1     429.9 76421 3017.7
## + test_prep:is_first_child                1      71.6 75920 3017.8
## + gender:transport_means                  1      66.1 75926 3017.9
## + gender:is_first_child                   1      59.1 75933 3017.9
## + gender:test_prep                        1      52.7 75939 3018.0
## + gender:lunch_type                       1       8.3 75983 3018.3
## + gender:practice_sport                   2     244.1 75748 3018.5
## + gender:wkly_study_hours                 2     240.2 75751 3018.5
## - ethnic_group:transport_means            4    1326.3 77318 3018.6
## + is_first_child:wkly_study_hours         2     213.2 75778 3018.7
## + transport_means:wkly_study_hours        2     158.8 75833 3019.1
## + practice_sport:transport_means          2      91.2 75900 3019.7
## + practice_sport:is_first_child           2      28.3 75963 3020.2
## + ethnic_group:lunch_type                 4     528.2 75463 3020.3
## + test_prep:parent_marital_status         3     219.9 75772 3020.7
## + ethnic_group:test_prep                  4     467.8 75524 3020.7
## + parent_educ:practice_sport             10    1968.3 74023 3020.9
## + lunch_type:parent_marital_status        3     163.3 75828 3021.1
## + ethnic_group:is_first_child             4     365.5 75626 3021.5
## - parent_marital_status:wkly_study_hours  6    2263.7 78255 3021.7
## + parent_educ:transport_means             5     583.3 75408 3021.8
## + gender:parent_marital_status            3      64.3 75927 3021.9
## + gender:ethnic_group                     4     233.9 75758 3022.6
## + gender:parent_educ                      5     453.0 75539 3022.8
## + parent_educ:lunch_type                  5     439.7 75552 3022.9
## - lunch_type:practice_sport               2    1447.7 77439 3023.5
## + parent_marital_status:practice_sport    6     544.3 75447 3024.1
## + ethnic_group:practice_sport             8    1040.0 74952 3024.2
## + parent_educ:wkly_study_hours           10    1447.2 74544 3025.0
## + parent_educ:test_prep                   5     136.2 75855 3025.3
## - parent_marital_status:is_first_child    3    1998.8 77990 3025.7
## + ethnic_group:parent_marital_status     11    1600.7 74391 3025.8
## + ethnic_group:wkly_study_hours           8     727.9 75264 3026.7
## + ethnic_group:parent_educ               20    2203.3 73788 3039.0
## - gender                                  1   12874.8 88866 3106.7
## 
## Step:  AIC=3015.44
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:practice_sport + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:is_first_child               1     112.2 77019 3014.3
## - is_first_child:transport_means          1     131.0 77038 3014.4
## - test_prep:transport_means               1     140.5 77048 3014.5
## - parent_educ:is_first_child              5    1213.8 78121 3014.7
## - test_prep:practice_sport                2     447.6 77355 3014.9
## <none>                                                76907 3015.4
## - test_prep:wkly_study_hours              2     530.7 77438 3015.5
## - lunch_type:wkly_study_hours             2     537.6 77445 3015.6
## - lunch_type:test_prep                    1     292.2 77199 3015.7
## - parent_marital_status:transport_means   3     855.9 77763 3016.0
## - parent_educ:parent_marital_status      15    4099.1 81006 3016.1
## - lunch_type:transport_means              1     378.0 77285 3016.3
## + practice_sport:wkly_study_hours         4     915.5 75992 3016.4
## + test_prep:is_first_child                1      98.9 76808 3016.7
## + gender:is_first_child                   1      98.6 76808 3016.7
## - ethnic_group:transport_means            4    1240.6 78148 3016.9
## + gender:practice_sport                   2     316.3 76591 3017.0
## + gender:transport_means                  1      46.6 76860 3017.1
## + gender:test_prep                        1      42.4 76865 3017.1
## + is_first_child:wkly_study_hours         2     284.8 76622 3017.2
## + gender:lunch_type                       1       6.1 76901 3017.4
## + gender:wkly_study_hours                 2     223.6 76683 3017.7
## + transport_means:wkly_study_hours        2     181.5 76726 3018.0
## + practice_sport:transport_means          2      74.7 76832 3018.9
## + practice_sport:is_first_child           2      50.1 76857 3019.1
## + ethnic_group:test_prep                  4     485.1 76422 3019.7
## + test_prep:parent_marital_status         3     175.0 76732 3020.1
## + ethnic_group:lunch_type                 4     427.3 76480 3020.2
## + parent_educ:transport_means             5     659.0 76248 3020.4
## + ethnic_group:is_first_child             4     398.8 76508 3020.4
## + lunch_type:parent_marital_status        3     136.8 76770 3020.4
## + gender:parent_marital_status            3      70.3 76837 3020.9
## + parent_educ:practice_sport             10    1831.0 75076 3021.2
## + parent_educ:lunch_type                  5     538.8 76368 3021.3
## - parent_marital_status:wkly_study_hours  6    2382.5 79290 3021.4
## + gender:parent_educ                      5     483.0 76424 3021.7
## + gender:ethnic_group                     4     222.0 76685 3021.7
## - lunch_type:practice_sport               2    1420.3 78327 3022.2
## + parent_marital_status:practice_sport    6     507.1 76400 3023.5
## + ethnic_group:practice_sport             8     971.4 75936 3023.9
## - parent_marital_status:is_first_child    3    1939.7 78847 3024.1
## + parent_educ:test_prep                   5     141.9 76765 3024.3
## + parent_educ:wkly_study_hours           10    1326.1 75581 3025.2
## + ethnic_group:wkly_study_hours           8     766.2 76141 3025.5
## + ethnic_group:parent_marital_status     11    1519.3 75388 3025.7
## + ethnic_group:parent_educ               20    2096.4 74811 3039.1
## - gender                                  1   12541.2 89448 3102.6
## 
## Step:  AIC=3014.3
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:transport_means               1     124.8 77144 3013.2
## - is_first_child:transport_means          1     128.6 77148 3013.3
## - parent_educ:is_first_child              5    1211.9 78231 3013.5
## - test_prep:practice_sport                2     461.2 77481 3013.8
## - test_prep:wkly_study_hours              2     519.7 77539 3014.3
## <none>                                                77019 3014.3
## - lunch_type:wkly_study_hours             2     554.4 77574 3014.5
## - lunch_type:test_prep                    1     300.8 77320 3014.6
## - parent_marital_status:transport_means   3     840.4 77860 3014.7
## - lunch_type:transport_means              1     363.1 77382 3015.1
## - parent_educ:parent_marital_status      15    4150.6 81170 3015.3
## + lunch_type:is_first_child               1     112.2 76907 3015.4
## + test_prep:is_first_child                1     111.9 76907 3015.4
## + gender:is_first_child                   1      87.1 76932 3015.6
## + practice_sport:wkly_study_hours         4     861.7 76158 3015.7
## + gender:practice_sport                   2     343.3 76676 3015.7
## - ethnic_group:transport_means            4    1239.7 78259 3015.7
## + is_first_child:wkly_study_hours         2     316.6 76703 3015.9
## + gender:transport_means                  1      38.4 76981 3016.0
## + gender:test_prep                        1      38.3 76981 3016.0
## + gender:lunch_type                       1       7.9 77011 3016.2
## + gender:wkly_study_hours                 2     220.2 76799 3016.6
## + transport_means:wkly_study_hours        2     189.0 76830 3016.8
## + practice_sport:transport_means          2      81.6 76938 3017.7
## + practice_sport:is_first_child           2      54.8 76965 3017.9
## + ethnic_group:test_prep                  4     488.8 76530 3018.5
## + ethnic_group:is_first_child             4     441.0 76578 3018.9
## + test_prep:parent_marital_status         3     175.7 76844 3018.9
## + ethnic_group:lunch_type                 4     416.5 76603 3019.1
## + lunch_type:parent_marital_status        3     133.8 76886 3019.3
## + parent_educ:transport_means             5     649.1 76370 3019.3
## + gender:parent_marital_status            3      64.9 76954 3019.8
## + parent_educ:practice_sport             10    1810.2 75209 3020.3
## + parent_educ:lunch_type                  5     522.4 76497 3020.3
## + gender:ethnic_group                     4     235.2 76784 3020.5
## + gender:parent_educ                      5     491.0 76528 3020.5
## - parent_marital_status:wkly_study_hours  6    2433.8 79453 3020.7
## - lunch_type:practice_sport               2    1430.6 78450 3021.2
## + ethnic_group:practice_sport             8     970.5 76049 3022.8
## + parent_marital_status:practice_sport    6     428.5 76591 3023.0
## + parent_educ:test_prep                   5     143.4 76876 3023.2
## - parent_marital_status:is_first_child    3    2057.4 79077 3023.8
## + parent_educ:wkly_study_hours           10    1304.5 75715 3024.2
## + ethnic_group:wkly_study_hours           8     774.1 76245 3024.3
## + ethnic_group:parent_marital_status     11    1464.4 75555 3025.0
## + ethnic_group:parent_educ               20    2101.3 74918 3038.0
## - gender                                  1   12517.3 89537 3101.2
## 
## Step:  AIC=3013.25
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - is_first_child:transport_means          1     144.1 77288 3012.3
## - parent_educ:is_first_child              5    1232.2 78376 3012.6
## - test_prep:practice_sport                2     465.7 77610 3012.8
## - lunch_type:wkly_study_hours             2     493.4 77638 3013.0
## - test_prep:wkly_study_hours              2     504.4 77648 3013.1
## <none>                                                77144 3013.2
## - lunch_type:test_prep                    1     306.8 77451 3013.6
## - parent_marital_status:transport_means   3     855.0 77999 3013.8
## - lunch_type:transport_means              1     345.9 77490 3013.9
## + test_prep:transport_means               1     124.8 77019 3014.3
## + test_prep:is_first_child                1     112.4 77032 3014.4
## + lunch_type:is_first_child               1      96.5 77048 3014.5
## + gender:is_first_child                   1      90.9 77053 3014.6
## + practice_sport:wkly_study_hours         4     867.3 76277 3014.6
## + is_first_child:wkly_study_hours         2     335.0 76809 3014.7
## + gender:practice_sport                   2     333.9 76810 3014.7
## - parent_educ:parent_marital_status      15    4230.9 81375 3014.8
## + gender:transport_means                  1      51.1 77093 3014.9
## + gender:test_prep                        1      33.7 77110 3015.0
## - ethnic_group:transport_means            4    1302.9 78447 3015.1
## + gender:lunch_type                       1      11.5 77133 3015.2
## + gender:wkly_study_hours                 2     229.6 76915 3015.5
## + transport_means:wkly_study_hours        2     164.7 76979 3016.0
## + practice_sport:transport_means          2      74.8 77069 3016.7
## + practice_sport:is_first_child           2      51.2 77093 3016.9
## + ethnic_group:test_prep                  4     518.1 76626 3017.3
## + test_prep:parent_marital_status         3     193.8 76950 3017.8
## + ethnic_group:lunch_type                 4     426.6 76718 3018.0
## + parent_educ:transport_means             5     682.3 76462 3018.0
## + ethnic_group:is_first_child             4     417.4 76727 3018.1
## + lunch_type:parent_marital_status        3     140.0 77004 3018.2
## + gender:parent_marital_status            3      62.0 77082 3018.8
## + parent_educ:lunch_type                  5     527.7 76616 3019.2
## + parent_educ:practice_sport             10    1795.9 75348 3019.3
## + gender:ethnic_group                     4     244.1 76900 3019.4
## + gender:parent_educ                      5     499.9 76644 3019.4
## - parent_marital_status:wkly_study_hours  6    2412.6 79557 3019.4
## - lunch_type:practice_sport               2    1455.1 78599 3020.3
## + ethnic_group:practice_sport             8     984.2 76160 3021.7
## + parent_marital_status:practice_sport    6     418.9 76725 3022.0
## + parent_educ:test_prep                   5     144.9 76999 3022.1
## - parent_marital_status:is_first_child    3    2069.6 79214 3022.9
## + parent_educ:wkly_study_hours           10    1307.3 75837 3023.2
## + ethnic_group:wkly_study_hours           8     770.1 76374 3023.3
## + ethnic_group:parent_marital_status     11    1459.7 75684 3024.0
## + ethnic_group:parent_educ               20    2023.1 75121 3037.6
## - gender                                  1   12401.3 89545 3099.2
## 
## Step:  AIC=3012.35
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:practice_sport                2     469.3 77757 3011.9
## - parent_educ:is_first_child              5    1272.3 78560 3012.0
## - test_prep:wkly_study_hours              2     508.1 77796 3012.2
## - lunch_type:wkly_study_hours             2     524.0 77812 3012.3
## <none>                                                77288 3012.3
## - lunch_type:test_prep                    1     272.9 77561 3012.4
## - lunch_type:transport_means              1     336.5 77625 3012.9
## + is_first_child:transport_means          1     144.1 77144 3013.2
## + test_prep:transport_means               1     140.3 77148 3013.3
## + test_prep:is_first_child                1     122.9 77165 3013.4
## + lunch_type:is_first_child               1      93.2 77195 3013.6
## + gender:practice_sport                   2     346.5 76942 3013.7
## - parent_marital_status:transport_means   3     971.0 78259 3013.7
## + gender:is_first_child                   1      78.7 77209 3013.8
## + practice_sport:wkly_study_hours         4     859.2 76429 3013.8
## - parent_educ:parent_marital_status      15    4238.5 81527 3013.8
## + gender:transport_means                  1      62.3 77226 3013.9
## + is_first_child:wkly_study_hours         2     301.1 76987 3014.1
## + gender:test_prep                        1      30.1 77258 3014.1
## + gender:lunch_type                       1       8.4 77280 3014.3
## - ethnic_group:transport_means            4    1313.4 78602 3014.3
## + gender:wkly_study_hours                 2     218.6 77070 3014.7
## + transport_means:wkly_study_hours        2     163.3 77125 3015.1
## + practice_sport:transport_means          2      89.4 77199 3015.7
## + practice_sport:is_first_child           2      64.9 77223 3015.9
## + ethnic_group:test_prep                  4     542.2 76746 3016.2
## + test_prep:parent_marital_status         3     183.1 77105 3016.9
## + ethnic_group:lunch_type                 4     413.2 76875 3017.2
## + lunch_type:parent_marital_status        3     139.1 77149 3017.3
## + parent_educ:transport_means             5     635.8 76652 3017.5
## + gender:parent_marital_status            3      80.3 77208 3017.7
## + ethnic_group:is_first_child             4     330.6 76958 3017.8
## + parent_educ:lunch_type                  5     529.8 76758 3018.3
## + gender:ethnic_group                     4     247.6 77041 3018.5
## + gender:parent_educ                      5     496.8 76791 3018.6
## - parent_marital_status:wkly_study_hours  6    2429.0 79717 3018.6
## + parent_educ:practice_sport             10    1711.9 75576 3019.1
## - lunch_type:practice_sport               2    1445.6 78734 3019.3
## + ethnic_group:practice_sport             8    1012.9 76275 3020.6
## + parent_educ:test_prep                   5     179.0 77109 3021.0
## + parent_marital_status:practice_sport    6     437.9 76850 3021.0
## - parent_marital_status:is_first_child    3    2038.1 79326 3021.7
## + parent_educ:wkly_study_hours           10    1301.9 75986 3022.3
## + ethnic_group:wkly_study_hours           8     781.1 76507 3022.4
## + ethnic_group:parent_marital_status     11    1531.4 75757 3022.6
## + ethnic_group:parent_educ               20    1990.8 75297 3037.0
## - gender                                  1   12297.8 89586 3097.5
## 
## Step:  AIC=3011.92
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:wkly_study_hours              2     503.4 78261 3011.7
## <none>                                                77757 3011.9
## - lunch_type:test_prep                    1     290.1 78048 3012.1
## - lunch_type:transport_means              1     318.4 78076 3012.3
## + test_prep:practice_sport                2     469.3 77288 3012.3
## - lunch_type:wkly_study_hours             2     588.6 78346 3012.4
## - parent_educ:parent_marital_status      15    4157.8 81915 3012.7
## + is_first_child:transport_means          1     147.6 77610 3012.8
## + test_prep:transport_means               1     145.3 77612 3012.8
## + test_prep:is_first_child                1     122.2 77635 3013.0
## + gender:practice_sport                   2     383.7 77374 3013.0
## - parent_educ:is_first_child              5    1477.9 79235 3013.0
## - parent_marital_status:transport_means   3     950.8 78708 3013.1
## + lunch_type:is_first_child               1     106.0 77652 3013.1
## + practice_sport:wkly_study_hours         4     891.5 76866 3013.1
## - ethnic_group:transport_means            4    1242.4 79000 3013.3
## + gender:is_first_child                   1      59.5 77698 3013.5
## + gender:transport_means                  1      54.2 77703 3013.5
## + gender:test_prep                        1      25.3 77732 3013.7
## + gender:lunch_type                       1      15.2 77742 3013.8
## + is_first_child:wkly_study_hours         2     265.7 77492 3013.9
## + transport_means:wkly_study_hours        2     199.8 77558 3014.4
## + gender:wkly_study_hours                 2     198.7 77559 3014.4
## + practice_sport:is_first_child           2      85.8 77672 3015.3
## + practice_sport:transport_means          2      82.6 77675 3015.3
## + test_prep:parent_marital_status         3     234.8 77523 3016.1
## + ethnic_group:lunch_type                 4     460.3 77297 3016.4
## + ethnic_group:test_prep                  4     451.0 77306 3016.5
## + lunch_type:parent_marital_status        3     142.6 77615 3016.8
## + parent_educ:transport_means             5     666.7 77091 3016.8
## + gender:parent_marital_status            3     101.5 77656 3017.2
## + ethnic_group:is_first_child             4     337.2 77420 3017.4
## - parent_marital_status:wkly_study_hours  6    2359.6 80117 3017.6
## + parent_educ:lunch_type                  5     553.5 77204 3017.7
## + gender:parent_educ                      5     531.7 77226 3017.9
## + gender:ethnic_group                     4     217.0 77540 3018.3
## + parent_educ:practice_sport             10    1673.0 76084 3019.1
## - lunch_type:practice_sport               2    1545.1 79303 3019.5
## - parent_marital_status:is_first_child    3    1928.4 79686 3020.4
## + ethnic_group:practice_sport             8     981.3 76776 3020.4
## + parent_marital_status:practice_sport    6     444.5 77313 3020.5
## + parent_educ:test_prep                   5     146.8 77611 3020.8
## + parent_educ:wkly_study_hours           10    1371.1 76386 3021.4
## + ethnic_group:wkly_study_hours           8     769.9 76988 3022.1
## + ethnic_group:parent_marital_status     11    1497.6 76260 3022.4
## + ethnic_group:parent_educ               20    2102.3 75655 3035.8
## - gender                                  1   12364.6 90122 3097.0
## 
## Step:  AIC=3011.73
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:transport_means              1     221.7 78483 3011.4
## <none>                                                78261 3011.7
## + test_prep:wkly_study_hours              2     503.4 77757 3011.9
## - parent_educ:parent_marital_status      15    4125.9 82387 3012.0
## - lunch_type:test_prep                    1     312.1 78573 3012.1
## + test_prep:practice_sport                2     464.6 77796 3012.2
## - ethnic_group:transport_means            4    1170.1 79431 3012.5
## + practice_sport:wkly_study_hours         4     942.3 77319 3012.6
## + is_first_child:transport_means          1     151.9 78109 3012.6
## - lunch_type:wkly_study_hours             2     649.4 78910 3012.6
## + test_prep:transport_means               1     129.4 78132 3012.8
## + test_prep:is_first_child                1     116.8 78144 3012.8
## - parent_marital_status:transport_means   3     952.4 79213 3012.9
## - parent_educ:is_first_child              5    1493.3 79754 3012.9
## + gender:practice_sport                   2     370.4 77890 3012.9
## + lunch_type:is_first_child               1      98.9 78162 3013.0
## + gender:transport_means                  1      60.3 78201 3013.3
## + gender:is_first_child                   1      51.3 78210 3013.3
## + gender:lunch_type                       1      22.1 78239 3013.6
## + gender:test_prep                        1      14.9 78246 3013.6
## + is_first_child:wkly_study_hours         2     273.1 77988 3013.7
## + gender:wkly_study_hours                 2     195.1 78066 3014.3
## + transport_means:wkly_study_hours        2     185.5 78075 3014.3
## + practice_sport:transport_means          2      85.5 78175 3015.1
## + practice_sport:is_first_child           2      56.2 78205 3015.3
## + ethnic_group:test_prep                  4     507.3 77754 3015.9
## + test_prep:parent_marital_status         3     218.3 78043 3016.1
## + ethnic_group:lunch_type                 4     477.5 77783 3016.1
## + parent_educ:transport_means             5     668.9 77592 3016.7
## + lunch_type:parent_marital_status        3     124.1 78137 3016.8
## + gender:parent_marital_status            3     110.8 78150 3016.9
## - parent_marital_status:wkly_study_hours  6    2347.2 80608 3017.2
## + gender:parent_educ                      5     531.0 77730 3017.7
## + parent_educ:lunch_type                  5     527.0 77734 3017.8
## + gender:ethnic_group                     4     259.9 78001 3017.8
## + ethnic_group:is_first_child             4     236.4 78024 3017.9
## - lunch_type:practice_sport               2    1430.9 79692 3018.4
## + parent_marital_status:practice_sport    6     469.5 77791 3020.2
## + parent_educ:practice_sport             10    1509.6 76751 3020.2
## + parent_educ:test_prep                   5     187.2 78074 3020.3
## + parent_educ:wkly_study_hours           10    1467.4 76794 3020.6
## - parent_marital_status:is_first_child    3    2024.8 80286 3020.8
## + ethnic_group:practice_sport             8     898.6 77362 3020.9
## + ethnic_group:parent_marital_status     11    1610.1 76651 3021.5
## + ethnic_group:wkly_study_hours           8     778.1 77483 3021.8
## + ethnic_group:parent_educ               20    2152.2 76109 3035.3
## - gender                                  1   12415.3 90676 3096.6
## 
## Step:  AIC=3011.4
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:test_prep                    1     262.1 78745 3011.4
## <none>                                                78483 3011.4
## - parent_educ:parent_marital_status      15    4130.4 82613 3011.7
## + lunch_type:transport_means              1     221.7 78261 3011.7
## + test_prep:practice_sport                2     449.9 78033 3012.0
## - ethnic_group:transport_means            4    1161.5 79644 3012.1
## - lunch_type:wkly_study_hours             2     628.3 79111 3012.1
## - parent_educ:is_first_child              5    1457.2 79940 3012.2
## + test_prep:is_first_child                1     146.9 78336 3012.3
## + is_first_child:transport_means          1     144.0 78339 3012.3
## + test_prep:wkly_study_hours              2     406.7 78076 3012.3
## + gender:practice_sport                   2     390.3 78092 3012.5
## + test_prep:transport_means               1     116.1 78367 3012.5
## - parent_marital_status:transport_means   3     954.6 79437 3012.5
## + practice_sport:wkly_study_hours         4     897.3 77585 3012.6
## + lunch_type:is_first_child               1      89.8 78393 3012.7
## + gender:transport_means                  1      71.0 78412 3012.9
## + gender:is_first_child                   1      67.6 78415 3012.9
## + gender:lunch_type                       1      31.1 78451 3013.2
## + gender:test_prep                        1      21.5 78461 3013.2
## + is_first_child:wkly_study_hours         2     272.3 78210 3013.3
## + gender:wkly_study_hours                 2     197.2 78285 3013.9
## + transport_means:wkly_study_hours        2     171.9 78311 3014.1
## + practice_sport:transport_means          2      92.0 78391 3014.7
## + practice_sport:is_first_child           2      53.0 78430 3015.0
## + ethnic_group:lunch_type                 4     533.7 77949 3015.4
## + ethnic_group:test_prep                  4     514.6 77968 3015.5
## + test_prep:parent_marital_status         3     224.0 78259 3015.7
## + gender:parent_marital_status            3     140.6 78342 3016.3
## + parent_educ:transport_means             5     664.5 77818 3016.4
## + lunch_type:parent_marital_status        3     128.4 78354 3016.4
## + gender:parent_educ                      5     587.5 77895 3017.0
## - parent_marital_status:wkly_study_hours  6    2395.3 80878 3017.1
## + parent_educ:lunch_type                  5     559.6 77923 3017.2
## + gender:ethnic_group                     4     256.9 78226 3017.5
## + ethnic_group:is_first_child             4     221.7 78261 3017.7
## - lunch_type:practice_sport               2    1393.9 79876 3017.8
## + parent_marital_status:practice_sport    6     467.3 78015 3019.9
## + parent_educ:test_prep                   5     194.3 78288 3019.9
## + parent_educ:practice_sport             10    1487.5 76995 3020.1
## + parent_educ:wkly_study_hours           10    1441.2 77041 3020.5
## - parent_marital_status:is_first_child    3    2065.7 80548 3020.7
## + ethnic_group:parent_marital_status     11    1648.0 76835 3020.9
## + ethnic_group:practice_sport             8     846.7 77636 3021.0
## + ethnic_group:wkly_study_hours           8     744.7 77738 3021.8
## + ethnic_group:parent_educ               20    2158.3 76324 3034.9
## - gender                                  1   12321.2 90804 3095.4
## 
## Step:  AIC=3011.37
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:practice_sport + lunch_type:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:parent_marital_status      15    4063.4 82808 3011.1
## <none>                                                78745 3011.4
## + lunch_type:test_prep                    1     262.1 78483 3011.4
## - lunch_type:wkly_study_hours             2     575.8 79321 3011.7
## + test_prep:practice_sport                2     468.3 78276 3011.8
## - parent_educ:is_first_child              5    1428.4 80173 3012.0
## - ethnic_group:transport_means            4    1168.4 79913 3012.1
## + lunch_type:transport_means              1     171.7 78573 3012.1
## + test_prep:wkly_study_hours              2     435.1 78310 3012.1
## + practice_sport:wkly_study_hours         4     949.3 77795 3012.2
## - parent_marital_status:transport_means   3     939.6 79684 3012.4
## + test_prep:is_first_child                1     129.3 78615 3012.4
## + test_prep:transport_means               1     121.3 78623 3012.5
## + gender:practice_sport                   2     386.6 78358 3012.5
## + is_first_child:transport_means          1     112.6 78632 3012.5
## + lunch_type:is_first_child               1     100.4 78644 3012.6
## + gender:is_first_child                   1      76.3 78668 3012.8
## + gender:transport_means                  1      74.0 78671 3012.8
## + gender:lunch_type                       1      46.0 78699 3013.0
## + is_first_child:wkly_study_hours         2     312.2 78432 3013.0
## + gender:test_prep                        1      29.1 78716 3013.2
## + gender:wkly_study_hours                 2     197.1 78548 3013.9
## + transport_means:wkly_study_hours        2     173.8 78571 3014.1
## + practice_sport:transport_means          2     114.1 78631 3014.5
## + practice_sport:is_first_child           2      62.2 78683 3014.9
## + ethnic_group:lunch_type                 4     561.7 78183 3015.1
## + ethnic_group:test_prep                  4     525.1 78220 3015.4
## + test_prep:parent_marital_status         3     228.3 78516 3015.7
## + parent_educ:transport_means             5     680.5 78064 3016.2
## + gender:parent_marital_status            3     140.2 78604 3016.3
## + lunch_type:parent_marital_status        3     119.1 78626 3016.5
## + gender:parent_educ                      5     618.2 78126 3016.7
## + parent_educ:lunch_type                  5     559.3 78185 3017.2
## - parent_marital_status:wkly_study_hours  6    2417.6 81162 3017.2
## + gender:ethnic_group                     4     269.6 78475 3017.3
## + ethnic_group:is_first_child             4     245.7 78499 3017.5
## - lunch_type:practice_sport               2    1369.3 80114 3017.5
## + parent_educ:practice_sport             10    1524.1 77221 3019.8
## + parent_educ:wkly_study_hours           10    1522.8 77222 3019.8
## + parent_marital_status:practice_sport    6     467.4 78277 3019.9
## + parent_educ:test_prep                   5     186.3 78558 3020.0
## + ethnic_group:practice_sport             8     913.7 77831 3020.5
## - parent_marital_status:is_first_child    3    2115.1 80860 3021.0
## + ethnic_group:wkly_study_hours           8     829.7 77915 3021.1
## + ethnic_group:parent_marital_status     11    1564.4 77180 3021.5
## + ethnic_group:parent_educ               20    2215.7 76529 3034.5
## - test_prep                               1    9863.4 88608 3079.0
## - gender                                  1   12254.8 91000 3094.7
## 
## Step:  AIC=3011.05
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:is_first_child + lunch_type:practice_sport + 
##     lunch_type:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_marital_status:transport_means   3     657.5 83466 3009.7
## - parent_educ:is_first_child              5    1407.4 84216 3011.0
## <none>                                                82808 3011.1
## + parent_educ:parent_marital_status      15    4063.4 78745 3011.4
## + test_prep:transport_means               1     195.2 82613 3011.7
## + lunch_type:test_prep                    1     195.1 82613 3011.7
## + gender:practice_sport                   2     473.7 82334 3011.7
## + lunch_type:transport_means              1     185.2 82623 3011.7
## - ethnic_group:transport_means            4    1252.3 84060 3011.9
## + lunch_type:is_first_child               1     148.1 82660 3012.0
## + is_first_child:transport_means          1     126.7 82681 3012.2
## + test_prep:is_first_child                1     126.1 82682 3012.2
## + test_prep:wkly_study_hours              2     396.1 82412 3012.2
## - lunch_type:wkly_study_hours             2     731.3 83539 3012.2
## + test_prep:practice_sport                2     380.1 82428 3012.3
## + gender:is_first_child                   1      70.3 82738 3012.6
## + is_first_child:wkly_study_hours         2     345.7 82462 3012.6
## + practice_sport:wkly_study_hours         4     881.8 81926 3012.7
## + gender:transport_means                  1      38.6 82770 3012.8
## + gender:lunch_type                       1      36.2 82772 3012.8
## + gender:test_prep                        1      12.1 82796 3013.0
## + gender:wkly_study_hours                 2     277.5 82531 3013.1
## + transport_means:wkly_study_hours        2     155.0 82653 3013.9
## + practice_sport:transport_means          2      76.8 82731 3014.5
## + gender:parent_educ                      5     878.7 81929 3014.8
## + practice_sport:is_first_child           2      21.4 82787 3014.9
## - parent_marital_status:wkly_study_hours  6    2271.7 85080 3015.0
## - lunch_type:practice_sport               2    1129.5 83938 3015.1
## + lunch_type:parent_marital_status        3     198.0 82610 3015.6
## + ethnic_group:test_prep                  4     455.0 82353 3015.8
## + parent_educ:wkly_study_hours           10    2108.4 80700 3015.8
## - parent_marital_status:is_first_child    3    1546.8 84355 3016.0
## + test_prep:parent_marital_status         3     138.0 82670 3016.1
## + gender:parent_marital_status            3     117.4 82691 3016.2
## + parent_educ:transport_means             5     654.1 82154 3016.4
## + gender:ethnic_group                     4     364.0 82444 3016.4
## + ethnic_group:lunch_type                 4     347.8 82460 3016.6
## + ethnic_group:is_first_child             4     240.9 82567 3017.3
## + parent_educ:lunch_type                  5     513.6 82295 3017.4
## + parent_marital_status:practice_sport    6     744.7 82063 3017.7
## + parent_educ:practice_sport             10    1768.3 81040 3018.3
## + parent_educ:test_prep                   5     292.1 82516 3019.0
## + ethnic_group:practice_sport             8    1100.3 81708 3019.2
## + ethnic_group:parent_marital_status     11    1823.4 80985 3019.9
## + ethnic_group:wkly_study_hours           8     839.1 81969 3021.1
## + ethnic_group:parent_educ               20    2212.2 80596 3035.1
## - test_prep                               1    9566.9 92375 3073.6
## - gender                                  1   12656.8 95465 3093.0
## 
## Step:  AIC=3009.72
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:is_first_child + lunch_type:practice_sport + 
##     lunch_type:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:is_first_child              5    1301.6 84767 3008.8
## <none>                                                83466 3009.7
## - ethnic_group:transport_means            4    1174.0 84640 3010.0
## + test_prep:transport_means               1     229.8 83236 3010.1
## + is_first_child:transport_means          1     215.1 83251 3010.2
## + lunch_type:test_prep                    1     186.9 83279 3010.4
## + lunch_type:transport_means              1     186.6 83279 3010.4
## - lunch_type:wkly_study_hours             2     708.4 84174 3010.7
## + lunch_type:is_first_child               1     131.4 83334 3010.8
## + test_prep:is_first_child                1     127.4 83338 3010.8
## + gender:practice_sport                   2     407.4 83058 3010.8
## + gender:is_first_child                   1      96.5 83369 3011.0
## + parent_marital_status:transport_means   3     657.5 82808 3011.1
## + test_prep:wkly_study_hours              2     375.5 83090 3011.1
## + test_prep:practice_sport                2     375.2 83090 3011.1
## + gender:transport_means                  1      31.2 83435 3011.5
## + gender:lunch_type                       1      24.1 83442 3011.6
## + gender:test_prep                        1      17.3 83448 3011.6
## + practice_sport:wkly_study_hours         4     858.9 82607 3011.6
## + gender:wkly_study_hours                 2     280.1 83186 3011.7
## + is_first_child:wkly_study_hours         2     278.3 83187 3011.8
## + parent_educ:parent_marital_status      15    3781.3 79684 3012.4
## - parent_marital_status:wkly_study_hours  6    2151.2 85617 3012.7
## + transport_means:wkly_study_hours        2     134.1 83332 3012.8
## + gender:parent_educ                      5     969.9 82496 3012.8
## + practice_sport:transport_means          2     108.4 83357 3012.9
## + practice_sport:is_first_child           2       9.9 83456 3013.7
## + test_prep:parent_marital_status         3     220.3 83245 3014.2
## + parent_educ:wkly_study_hours           10    2160.5 81305 3014.2
## + lunch_type:parent_marital_status        3     191.9 83274 3014.4
## - lunch_type:practice_sport               2    1249.9 84716 3014.5
## + gender:parent_marital_status            3     129.0 83337 3014.8
## + gender:ethnic_group                     4     409.1 83057 3014.8
## + ethnic_group:test_prep                  4     400.2 83065 3014.9
## - parent_marital_status:is_first_child    3    1618.7 85084 3015.1
## + parent_educ:transport_means             5     613.7 82852 3015.4
## + ethnic_group:lunch_type                 4     331.8 83134 3015.4
## + parent_educ:lunch_type                  5     499.0 82967 3016.2
## + parent_educ:practice_sport             10    1891.8 81574 3016.2
## + ethnic_group:is_first_child             4     190.0 83276 3016.4
## + parent_marital_status:practice_sport    6     751.8 82714 3016.4
## + ethnic_group:practice_sport             8    1191.8 82274 3017.2
## + parent_educ:test_prep                   5     302.8 83163 3017.6
## + ethnic_group:parent_marital_status     11    1930.5 81535 3017.9
## + ethnic_group:wkly_study_hours           8     816.2 82649 3019.9
## + ethnic_group:parent_educ               20    2008.0 81458 3035.3
## - test_prep                               1    9947.6 93413 3074.2
## - gender                                  1   12642.9 96109 3090.9
## 
## Step:  AIC=3008.85
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     lunch_type:practice_sport + lunch_type:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## <none>                                                84767 3008.8
## + test_prep:transport_means               1     263.6 84504 3009.0
## + test_prep:practice_sport                2     543.3 84224 3009.1
## + is_first_child:transport_means          1     254.5 84513 3009.1
## - ethnic_group:transport_means            4    1232.7 86000 3009.4
## - lunch_type:wkly_study_hours             2     680.0 85447 3009.6
## + lunch_type:test_prep                    1     164.4 84603 3009.7
## + parent_educ:is_first_child              5    1301.6 83466 3009.7
## + lunch_type:transport_means              1     139.2 84628 3009.9
## + lunch_type:is_first_child               1     125.4 84642 3010.0
## + gender:practice_sport                   2     401.7 84366 3010.1
## + gender:is_first_child                   1     108.5 84659 3010.1
## + test_prep:wkly_study_hours              2     383.2 84384 3010.2
## + test_prep:is_first_child                1      63.8 84704 3010.4
## + gender:lunch_type                       1      22.9 84744 3010.7
## + gender:transport_means                  1      19.0 84748 3010.7
## + gender:test_prep                        1       5.3 84762 3010.8
## + parent_marital_status:transport_means   3     551.7 84216 3011.0
## - parent_marital_status:wkly_study_hours  6    2060.3 86828 3011.0
## + gender:wkly_study_hours                 2     232.3 84535 3011.2
## + is_first_child:wkly_study_hours         2     193.2 84574 3011.5
## + parent_educ:parent_marital_status      15    3818.8 80949 3011.7
## + transport_means:wkly_study_hours        2     107.3 84660 3012.1
## + practice_sport:transport_means          2     103.2 84664 3012.1
## + practice_sport:wkly_study_hours         4     671.8 84096 3012.2
## - parent_marital_status:is_first_child    3    1395.1 86162 3012.5
## + gender:parent_educ                      5     882.7 83885 3012.7
## + practice_sport:is_first_child           2       3.9 84763 3012.8
## + test_prep:parent_marital_status         3     189.7 84578 3013.5
## - lunch_type:practice_sport               2    1258.7 86026 3013.6
## + ethnic_group:test_prep                  4     470.3 84297 3013.6
## + lunch_type:parent_marital_status        3     184.0 84583 3013.6
## + gender:ethnic_group                     4     464.8 84303 3013.6
## + parent_educ:practice_sport             10    2151.4 82616 3013.7
## + ethnic_group:lunch_type                 4     388.3 84379 3014.1
## + gender:parent_marital_status            3      70.7 84697 3014.4
## + parent_educ:wkly_study_hours           10    2035.7 82732 3014.5
## + parent_educ:transport_means             5     615.3 84152 3014.6
## + parent_marital_status:practice_sport    6     773.3 83994 3015.4
## + parent_educ:lunch_type                  5     477.7 84290 3015.5
## + ethnic_group:is_first_child             4     188.4 84579 3015.5
## + parent_educ:test_prep                   5     338.3 84429 3016.5
## + ethnic_group:practice_sport             8    1107.8 83660 3017.1
## + ethnic_group:parent_marital_status     11    1856.5 82911 3017.8
## + ethnic_group:wkly_study_hours           8     765.8 84002 3019.5
## + ethnic_group:parent_educ               20    2002.1 82765 3034.8
## - parent_educ                             5    9294.5 94062 3060.2
## - test_prep                               1    9780.6 94548 3071.3
## - gender                                  1   12516.7 97284 3088.1
summary(stepwise_model_write)
## 
## Call:
## lm(formula = writing_score ~ gender + ethnic_group + parent_educ + 
##     lunch_type + test_prep + parent_marital_status + practice_sport + 
##     is_first_child + transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     lunch_type:practice_sport + lunch_type:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours, 
##     data = df_4_mdl_write)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -48.763  -7.903   0.888   8.581  28.915 
## 
## Coefficients:
##                                                      Estimate Std. Error
## (Intercept)                                          67.70191    5.43878
## gendermale                                           -9.60342    1.06468
## ethnic_groupgroup B                                   2.66505    3.60266
## ethnic_groupgroup C                                   4.66371    3.29737
## ethnic_groupgroup D                                   6.89890    3.37504
## ethnic_groupgroup E                                  12.97757    3.72825
## parent_educbachelor's degree                          3.78448    1.87145
## parent_educhigh school                               -6.78406    1.62165
## parent_educmaster's degree                            5.13686    2.33681
## parent_educsome college                              -1.61594    1.62678
## parent_educsome high school                          -6.56468    1.63632
## lunch_typestandard                                    1.01145    3.66619
## test_prepnone                                        -8.81344    1.10535
## parent_marital_statusmarried                          7.41012    3.91977
## parent_marital_statussingle                          -3.99879    4.28335
## parent_marital_statuswidowed                         12.38775   10.44238
## practice_sportregularly                              -3.44862    3.11402
## practice_sportsometimes                              -5.25858    3.01623
## is_first_childyes                                     6.17523    3.24819
## transport_meansschool_bus                             5.99682    3.71242
## wkly_study_hours> 10                                -13.41677    4.87463
## wkly_study_hours10-May                               -1.32300    3.52689
## ethnic_groupgroup B:transport_meansschool_bus        -6.38307    4.47966
## ethnic_groupgroup C:transport_meansschool_bus        -7.47646    4.19267
## ethnic_groupgroup D:transport_meansschool_bus        -2.44868    4.26882
## ethnic_groupgroup E:transport_meansschool_bus       -10.30293    4.71351
## lunch_typestandard:practice_sportregularly            6.16137    3.77036
## lunch_typestandard:practice_sportsometimes           10.02195    3.67485
## lunch_typestandard:wkly_study_hours> 10               5.91877    3.33331
## lunch_typestandard:wkly_study_hours10-May            -0.07475    2.59512
## parent_marital_statusmarried:is_first_childyes       -7.62546    3.55928
## parent_marital_statussingle:is_first_childyes        -0.73567    3.95710
## parent_marital_statuswidowed:is_first_childyes       -5.74724    8.37846
## parent_marital_statusmarried:wkly_study_hours> 10    10.26572    4.74053
## parent_marital_statussingle:wkly_study_hours> 10     18.67985    5.30411
## parent_marital_statuswidowed:wkly_study_hours> 10     5.92668   13.84492
## parent_marital_statusmarried:wkly_study_hours10-May   3.32999    3.53309
## parent_marital_statussingle:wkly_study_hours10-May    8.29920    3.98905
## parent_marital_statuswidowed:wkly_study_hours10-May  -0.28438   10.39843
##                                                     t value Pr(>|t|)    
## (Intercept)                                          12.448  < 2e-16 ***
## gendermale                                           -9.020  < 2e-16 ***
## ethnic_groupgroup B                                   0.740 0.459770    
## ethnic_groupgroup C                                   1.414 0.157818    
## ethnic_groupgroup D                                   2.044 0.041419 *  
## ethnic_groupgroup E                                   3.481 0.000539 ***
## parent_educbachelor's degree                          2.022 0.043636 *  
## parent_educhigh school                               -4.183 3.34e-05 ***
## parent_educmaster's degree                            2.198 0.028347 *  
## parent_educsome college                              -0.993 0.320980    
## parent_educsome high school                          -4.012 6.86e-05 ***
## lunch_typestandard                                    0.276 0.782738    
## test_prepnone                                        -7.973 8.95e-15 ***
## parent_marital_statusmarried                          1.890 0.059222 .  
## parent_marital_statussingle                          -0.934 0.350937    
## parent_marital_statuswidowed                          1.186 0.236016    
## practice_sportregularly                              -1.107 0.268583    
## practice_sportsometimes                              -1.743 0.081816 .  
## is_first_childyes                                     1.901 0.057806 .  
## transport_meansschool_bus                             1.615 0.106809    
## wkly_study_hours> 10                                 -2.752 0.006112 ** 
## wkly_study_hours10-May                               -0.375 0.707718    
## ethnic_groupgroup B:transport_meansschool_bus        -1.425 0.154752    
## ethnic_groupgroup C:transport_meansschool_bus        -1.783 0.075100 .  
## ethnic_groupgroup D:transport_meansschool_bus        -0.574 0.566459    
## ethnic_groupgroup E:transport_meansschool_bus        -2.186 0.029248 *  
## lunch_typestandard:practice_sportregularly            1.634 0.102796    
## lunch_typestandard:practice_sportsometimes            2.727 0.006592 ** 
## lunch_typestandard:wkly_study_hours> 10               1.776 0.076344 .  
## lunch_typestandard:wkly_study_hours10-May            -0.029 0.977030    
## parent_marital_statusmarried:is_first_childyes       -2.142 0.032597 *  
## parent_marital_statussingle:is_first_childyes        -0.186 0.852583    
## parent_marital_statuswidowed:is_first_childyes       -0.686 0.493030    
## parent_marital_statusmarried:wkly_study_hours> 10     2.166 0.030776 *  
## parent_marital_statussingle:wkly_study_hours> 10      3.522 0.000464 ***
## parent_marital_statuswidowed:wkly_study_hours> 10     0.428 0.668763    
## parent_marital_statusmarried:wkly_study_hours10-May   0.943 0.346342    
## parent_marital_statussingle:wkly_study_hours10-May    2.080 0.037941 *  
## parent_marital_statuswidowed:wkly_study_hours10-May  -0.027 0.978192    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 12.4 on 551 degrees of freedom
## Multiple R-squared:  0.4032, Adjusted R-squared:  0.362 
## F-statistic: 9.796 on 38 and 551 DF,  p-value: < 2.2e-16

MAth Score

df_4_mdl_math=test_df %>% dplyr::select(gender,ethnic_group,parent_educ,lunch_type,test_prep,parent_marital_status,practice_sport,is_first_child,transport_means,wkly_study_hours,math_score)
full_fit_math=lm(math_score ~ .^2,data=df_4_mdl_math)
summary(full_fit_math)
## 
## Call:
## lm(formula = math_score ~ .^2, data = df_4_mdl_math)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -37.489  -7.390   0.168   7.221  24.154 
## 
## Coefficients: (4 not defined because of singularities)
##                                                            Estimate Std. Error
## (Intercept)                                                 68.0411    17.6110
## gendermale                                                   4.9827     8.9723
## ethnic_groupgroup B                                        -20.0944    15.1422
## ethnic_groupgroup C                                        -26.3767    14.2851
## ethnic_groupgroup D                                        -16.7609    15.5502
## ethnic_groupgroup E                                         -2.1592    14.5735
## parent_educbachelor's degree                                33.6079    15.9209
## parent_educhigh school                                      12.3061    13.1796
## parent_educmaster's degree                                 -25.1426    21.7572
## parent_educsome college                                     -3.3640    12.9319
## parent_educsome high school                                  1.5736    12.5441
## lunch_typestandard                                           2.2940     8.9077
## test_prepnone                                              -16.5825     9.2941
## parent_marital_statusmarried                                11.4586    11.8338
## parent_marital_statussingle                                  7.8399    14.2425
## parent_marital_statuswidowed                                56.5536    42.0759
## practice_sportregularly                                    -29.8202    14.1677
## practice_sportsometimes                                    -20.2458    14.0961
## is_first_childyes                                           13.1687    10.2054
## transport_meansschool_bus                                   -3.8403     9.0340
## wkly_study_hours> 10                                       -10.7976    13.9166
## wkly_study_hours10-May                                       4.6821    11.1838
## gendermale:ethnic_groupgroup B                               5.2886     5.6833
## gendermale:ethnic_groupgroup C                              10.1735     5.4655
## gendermale:ethnic_groupgroup D                               4.3097     5.4293
## gendermale:ethnic_groupgroup E                               6.3964     6.0199
## gendermale:parent_educbachelor's degree                     -4.5741     4.7806
## gendermale:parent_educhigh school                            1.1545     3.8987
## gendermale:parent_educmaster's degree                       11.0840     6.6935
## gendermale:parent_educsome college                          -4.4251     4.0942
## gendermale:parent_educsome high school                       1.5882     4.0216
## gendermale:lunch_typestandard                               -2.4581     2.7927
## gendermale:test_prepnone                                     0.3238     2.7833
## gendermale:parent_marital_statusmarried                     -2.2028     3.9676
## gendermale:parent_marital_statussingle                      -1.7229     4.4981
## gendermale:parent_marital_statuswidowed                     -1.1049    19.4773
## gendermale:practice_sportregularly                          -3.5415     4.7295
## gendermale:practice_sportsometimes                          -3.5726     4.7543
## gendermale:is_first_childyes                                 2.6976     2.9215
## gendermale:transport_meansschool_bus                        -0.3742     2.7006
## gendermale:wkly_study_hours> 10                             -3.4820     4.2367
## gendermale:wkly_study_hours10-May                           -1.9685     3.2131
## ethnic_groupgroup B:parent_educbachelor's degree            -4.2231    13.2581
## ethnic_groupgroup C:parent_educbachelor's degree            -3.7714    13.2368
## ethnic_groupgroup D:parent_educbachelor's degree            -1.2605    13.1369
## ethnic_groupgroup E:parent_educbachelor's degree            -9.8679    14.9506
## ethnic_groupgroup B:parent_educhigh school                 -12.1115     8.3005
## ethnic_groupgroup C:parent_educhigh school                  -7.8179     7.9780
## ethnic_groupgroup D:parent_educhigh school                  -4.1223     8.1111
## ethnic_groupgroup E:parent_educhigh school                  -7.1674     9.0331
## ethnic_groupgroup B:parent_educmaster's degree               6.1658    15.9289
## ethnic_groupgroup C:parent_educmaster's degree              -5.7091    14.7953
## ethnic_groupgroup D:parent_educmaster's degree               2.3388    15.0307
## ethnic_groupgroup E:parent_educmaster's degree              -0.8632    15.8151
## ethnic_groupgroup B:parent_educsome college                  2.3899     9.1796
## ethnic_groupgroup C:parent_educsome college                  3.2541     8.6646
## ethnic_groupgroup D:parent_educsome college                 12.0158     9.0246
## ethnic_groupgroup E:parent_educsome college                  1.8215     9.1236
## ethnic_groupgroup B:parent_educsome high school            -15.0749     8.7983
## ethnic_groupgroup C:parent_educsome high school             -4.9385     8.2551
## ethnic_groupgroup D:parent_educsome high school             -1.1085     8.3094
## ethnic_groupgroup E:parent_educsome high school              2.2394     8.9218
## ethnic_groupgroup B:lunch_typestandard                       3.7732     5.9098
## ethnic_groupgroup C:lunch_typestandard                       7.9926     5.7317
## ethnic_groupgroup D:lunch_typestandard                       4.4950     5.6419
## ethnic_groupgroup E:lunch_typestandard                       0.8425     6.5383
## ethnic_groupgroup B:test_prepnone                            2.4360     6.0294
## ethnic_groupgroup C:test_prepnone                            7.7889     5.6560
## ethnic_groupgroup D:test_prepnone                            7.7952     5.6674
## ethnic_groupgroup E:test_prepnone                           11.4896     6.1691
## ethnic_groupgroup B:parent_marital_statusmarried             4.5004     8.1401
## ethnic_groupgroup C:parent_marital_statusmarried             2.5638     7.4956
## ethnic_groupgroup D:parent_marital_statusmarried            -8.5771     7.3930
## ethnic_groupgroup E:parent_marital_statusmarried            -2.5010     8.1793
## ethnic_groupgroup B:parent_marital_statussingle             11.3279     9.6376
## ethnic_groupgroup C:parent_marital_statussingle              3.2686     9.1120
## ethnic_groupgroup D:parent_marital_statussingle             -2.3267     8.8048
## ethnic_groupgroup E:parent_marital_statussingle              6.0944    10.1485
## ethnic_groupgroup B:parent_marital_statuswidowed           112.2530   107.8327
## ethnic_groupgroup C:parent_marital_statuswidowed           143.7513    87.6384
## ethnic_groupgroup D:parent_marital_statuswidowed            31.6392    88.3465
## ethnic_groupgroup E:parent_marital_statuswidowed                 NA         NA
## ethnic_groupgroup B:practice_sportregularly                 18.1643    10.7978
## ethnic_groupgroup C:practice_sportregularly                 15.6305    10.7005
## ethnic_groupgroup D:practice_sportregularly                 15.7111    11.9445
## ethnic_groupgroup E:practice_sportregularly                 16.2136    10.9347
## ethnic_groupgroup B:practice_sportsometimes                 12.2733    11.5184
## ethnic_groupgroup C:practice_sportsometimes                 18.8952    11.2034
## ethnic_groupgroup D:practice_sportsometimes                 12.8401    12.3508
## ethnic_groupgroup E:practice_sportsometimes                 11.3892    11.2604
## ethnic_groupgroup B:is_first_childyes                       10.2091     5.9835
## ethnic_groupgroup C:is_first_childyes                       -0.1812     5.6444
## ethnic_groupgroup D:is_first_childyes                        1.1359     5.7099
## ethnic_groupgroup E:is_first_childyes                        3.4944     6.4312
## ethnic_groupgroup B:transport_meansschool_bus               -4.0964     5.9868
## ethnic_groupgroup C:transport_meansschool_bus              -10.1575     5.5281
## ethnic_groupgroup D:transport_meansschool_bus               -2.9759     5.5226
## ethnic_groupgroup E:transport_meansschool_bus              -11.7574     6.5192
## ethnic_groupgroup B:wkly_study_hours> 10                   -10.0294    10.1919
## ethnic_groupgroup C:wkly_study_hours> 10                     1.4113    10.0649
## ethnic_groupgroup D:wkly_study_hours> 10                     4.1762    10.0509
## ethnic_groupgroup E:wkly_study_hours> 10                    -3.4964    10.9491
## ethnic_groupgroup B:wkly_study_hours10-May                  -5.9718     8.5598
## ethnic_groupgroup C:wkly_study_hours10-May                   2.3955     8.3758
## ethnic_groupgroup D:wkly_study_hours10-May                   2.5625     8.5173
## ethnic_groupgroup E:wkly_study_hours10-May                  -2.6577     9.1705
## parent_educbachelor's degree:lunch_typestandard              2.1141     5.1441
## parent_educhigh school:lunch_typestandard                    0.3684     4.1512
## parent_educmaster's degree:lunch_typestandard                9.9274     7.6084
## parent_educsome college:lunch_typestandard                   3.3042     4.1848
## parent_educsome high school:lunch_typestandard               5.5345     4.3349
## parent_educbachelor's degree:test_prepnone                  -3.9833     4.7464
## parent_educhigh school:test_prepnone                        -1.1824     4.5458
## parent_educmaster's degree:test_prepnone                    -1.8200     8.0921
## parent_educsome college:test_prepnone                       -2.3529     4.2606
## parent_educsome high school:test_prepnone                    3.0111     4.1206
## parent_educbachelor's degree:parent_marital_statusmarried  -17.7590     8.4713
## parent_educhigh school:parent_marital_statusmarried          1.5718     5.9578
## parent_educmaster's degree:parent_marital_statusmarried      2.1560     8.6196
## parent_educsome college:parent_marital_statusmarried        -8.3928     5.8669
## parent_educsome high school:parent_marital_statusmarried    -7.8355     5.7817
## parent_educbachelor's degree:parent_marital_statussingle   -19.7203     9.1319
## parent_educhigh school:parent_marital_statussingle           3.9993     6.5081
## parent_educmaster's degree:parent_marital_statussingle      -1.7191     9.2012
## parent_educsome college:parent_marital_statussingle         -9.4469     6.5341
## parent_educsome high school:parent_marital_statussingle     -9.7176     6.4548
## parent_educbachelor's degree:parent_marital_statuswidowed  -38.7612    89.7785
## parent_educhigh school:parent_marital_statuswidowed       -117.8054    98.7809
## parent_educmaster's degree:parent_marital_statuswidowed   -110.3756    51.7457
## parent_educsome college:parent_marital_statuswidowed      -114.0106    64.8797
## parent_educsome high school:parent_marital_statuswidowed   -92.5395    77.7614
## parent_educbachelor's degree:practice_sportregularly        -3.7294     8.7461
## parent_educhigh school:practice_sportregularly             -13.6445     7.5268
## parent_educmaster's degree:practice_sportregularly           0.7016    10.6360
## parent_educsome college:practice_sportregularly             -0.2142     7.6542
## parent_educsome high school:practice_sportregularly         -2.7852     7.3917
## parent_educbachelor's degree:practice_sportsometimes       -12.4201     8.3926
## parent_educhigh school:practice_sportsometimes             -13.5033     7.1288
## parent_educmaster's degree:practice_sportsometimes           9.0615     8.8601
## parent_educsome college:practice_sportsometimes              1.2774     7.3663
## parent_educsome high school:practice_sportsometimes          0.4391     6.9262
## parent_educbachelor's degree:is_first_childyes               2.0649     5.1938
## parent_educhigh school:is_first_childyes                     8.6134     4.4335
## parent_educmaster's degree:is_first_childyes                 6.7664     7.7546
## parent_educsome college:is_first_childyes                    9.2132     4.3295
## parent_educsome high school:is_first_childyes                4.6542     4.3602
## parent_educbachelor's degree:transport_meansschool_bus       5.4304     5.1849
## parent_educhigh school:transport_meansschool_bus             4.0937     4.1394
## parent_educmaster's degree:transport_meansschool_bus        11.6831     6.3824
## parent_educsome college:transport_meansschool_bus            4.9041     4.2151
## parent_educsome high school:transport_meansschool_bus        6.9767     4.2890
## parent_educbachelor's degree:wkly_study_hours> 10          -14.7410     7.6498
## parent_educhigh school:wkly_study_hours> 10                -10.1303     6.3679
## parent_educmaster's degree:wkly_study_hours> 10              6.3671    13.7791
## parent_educsome college:wkly_study_hours> 10                -7.2539     6.4097
## parent_educsome high school:wkly_study_hours> 10           -11.3467     6.5283
## parent_educbachelor's degree:wkly_study_hours10-May         -3.4329     5.3169
## parent_educhigh school:wkly_study_hours10-May               -9.6586     4.9571
## parent_educmaster's degree:wkly_study_hours10-May            0.9849     7.0888
## parent_educsome college:wkly_study_hours10-May              -3.5554     5.0476
## parent_educsome high school:wkly_study_hours10-May         -10.4143     5.3257
## lunch_typestandard:test_prepnone                            -1.9452     3.1136
## lunch_typestandard:parent_marital_statusmarried             -6.2756     4.0742
## lunch_typestandard:parent_marital_statussingle              -2.2019     4.7175
## lunch_typestandard:parent_marital_statuswidowed            -21.8879    80.6364
## lunch_typestandard:practice_sportregularly                  10.3501     5.3704
## lunch_typestandard:practice_sportsometimes                  11.0341     5.1768
## lunch_typestandard:is_first_childyes                         0.1283     3.1548
## lunch_typestandard:transport_meansschool_bus                -2.5076     2.8951
## lunch_typestandard:wkly_study_hours> 10                      5.7376     4.4178
## lunch_typestandard:wkly_study_hours10-May                    0.5929     3.3046
## test_prepnone:parent_marital_statusmarried                   5.6467     4.1442
## test_prepnone:parent_marital_statussingle                    2.5438     4.7712
## test_prepnone:parent_marital_statuswidowed                 -70.1691    42.1289
## test_prepnone:practice_sportregularly                        1.5825     5.1802
## test_prepnone:practice_sportsometimes                        3.1630     5.0767
## test_prepnone:is_first_childyes                             -0.6723     3.1267
## test_prepnone:transport_meansschool_bus                      0.4150     2.8429
## test_prepnone:wkly_study_hours> 10                          -4.6995     4.4626
## test_prepnone:wkly_study_hours10-May                         1.6772     3.5219
## parent_marital_statusmarried:practice_sportregularly         9.1006     6.6592
## parent_marital_statussingle:practice_sportregularly          2.6152     8.7085
## parent_marital_statuswidowed:practice_sportregularly        22.5587    85.2725
## parent_marital_statusmarried:practice_sportsometimes         5.1124     6.5673
## parent_marital_statussingle:practice_sportsometimes         -1.6116     8.5136
## parent_marital_statuswidowed:practice_sportsometimes             NA         NA
## parent_marital_statusmarried:is_first_childyes             -12.7542     4.8986
## parent_marital_statussingle:is_first_childyes               -4.9445     5.4292
## parent_marital_statuswidowed:is_first_childyes              47.8196    30.2193
## parent_marital_statusmarried:transport_meansschool_bus       4.6203     4.0454
## parent_marital_statussingle:transport_meansschool_bus       -2.0235     4.6103
## parent_marital_statuswidowed:transport_meansschool_bus     -34.0699    19.6388
## parent_marital_statusmarried:wkly_study_hours> 10           18.1048     6.3197
## parent_marital_statussingle:wkly_study_hours> 10            21.8022     7.0282
## parent_marital_statuswidowed:wkly_study_hours> 10                NA         NA
## parent_marital_statusmarried:wkly_study_hours10-May          1.2179     4.6394
## parent_marital_statussingle:wkly_study_hours10-May           3.3543     5.1241
## parent_marital_statuswidowed:wkly_study_hours10-May              NA         NA
## practice_sportregularly:is_first_childyes                   -3.3085     6.0157
## practice_sportsometimes:is_first_childyes                   -5.4272     5.8699
## practice_sportregularly:transport_meansschool_bus            9.9774     5.0267
## practice_sportsometimes:transport_meansschool_bus            5.9885     4.8789
## practice_sportregularly:wkly_study_hours> 10                 2.6252     7.1266
## practice_sportsometimes:wkly_study_hours> 10                 2.0680     6.9901
## practice_sportregularly:wkly_study_hours10-May               7.8713     5.4844
## practice_sportsometimes:wkly_study_hours10-May               2.5781     5.4074
## is_first_childyes:transport_meansschool_bus                 -5.3887     3.0599
## is_first_childyes:wkly_study_hours> 10                       2.8322     4.6001
## is_first_childyes:wkly_study_hours10-May                    -4.9634     3.4724
## transport_meansschool_bus:wkly_study_hours> 10               4.0303     4.4205
## transport_meansschool_bus:wkly_study_hours10-May             2.7910     3.1920
##                                                           t value Pr(>|t|)    
## (Intercept)                                                 3.864 0.000131 ***
## gendermale                                                  0.555 0.578989    
## ethnic_groupgroup B                                        -1.327 0.185283    
## ethnic_groupgroup C                                        -1.846 0.065599 .  
## ethnic_groupgroup D                                        -1.078 0.281775    
## ethnic_groupgroup E                                        -0.148 0.882295    
## parent_educbachelor's degree                                2.111 0.035426 *  
## parent_educhigh school                                      0.934 0.351036    
## parent_educmaster's degree                                 -1.156 0.248565    
## parent_educsome college                                    -0.260 0.794902    
## parent_educsome high school                                 0.125 0.900238    
## lunch_typestandard                                          0.258 0.796904    
## test_prepnone                                              -1.784 0.075183 .  
## parent_marital_statusmarried                                0.968 0.333510    
## parent_marital_statussingle                                 0.550 0.582326    
## parent_marital_statuswidowed                                1.344 0.179717    
## practice_sportregularly                                    -2.105 0.035959 *  
## practice_sportsometimes                                    -1.436 0.151741    
## is_first_childyes                                           1.290 0.197701    
## transport_meansschool_bus                                  -0.425 0.671008    
## wkly_study_hours> 10                                       -0.776 0.438299    
## wkly_study_hours10-May                                      0.419 0.675703    
## gendermale:ethnic_groupgroup B                              0.931 0.352678    
## gendermale:ethnic_groupgroup C                              1.861 0.063454 .  
## gendermale:ethnic_groupgroup D                              0.794 0.427811    
## gendermale:ethnic_groupgroup E                              1.063 0.288659    
## gendermale:parent_educbachelor's degree                    -0.957 0.339269    
## gendermale:parent_educhigh school                           0.296 0.767289    
## gendermale:parent_educmaster's degree                       1.656 0.098552 .  
## gendermale:parent_educsome college                         -1.081 0.280453    
## gendermale:parent_educsome high school                      0.395 0.693115    
## gendermale:lunch_typestandard                              -0.880 0.379317    
## gendermale:test_prepnone                                    0.116 0.907448    
## gendermale:parent_marital_statusmarried                    -0.555 0.579095    
## gendermale:parent_marital_statussingle                     -0.383 0.701904    
## gendermale:parent_marital_statuswidowed                    -0.057 0.954790    
## gendermale:practice_sportregularly                         -0.749 0.454437    
## gendermale:practice_sportsometimes                         -0.751 0.452841    
## gendermale:is_first_childyes                                0.923 0.356397    
## gendermale:transport_meansschool_bus                       -0.139 0.889859    
## gendermale:wkly_study_hours> 10                            -0.822 0.411658    
## gendermale:wkly_study_hours10-May                          -0.613 0.540476    
## ethnic_groupgroup B:parent_educbachelor's degree           -0.319 0.750255    
## ethnic_groupgroup C:parent_educbachelor's degree           -0.285 0.775863    
## ethnic_groupgroup D:parent_educbachelor's degree           -0.096 0.923607    
## ethnic_groupgroup E:parent_educbachelor's degree           -0.660 0.509629    
## ethnic_groupgroup B:parent_educhigh school                 -1.459 0.145350    
## ethnic_groupgroup C:parent_educhigh school                 -0.980 0.327741    
## ethnic_groupgroup D:parent_educhigh school                 -0.508 0.611582    
## ethnic_groupgroup E:parent_educhigh school                 -0.793 0.428002    
## ethnic_groupgroup B:parent_educmaster's degree              0.387 0.698911    
## ethnic_groupgroup C:parent_educmaster's degree             -0.386 0.699808    
## ethnic_groupgroup D:parent_educmaster's degree              0.156 0.876431    
## ethnic_groupgroup E:parent_educmaster's degree             -0.055 0.956503    
## ethnic_groupgroup B:parent_educsome college                 0.260 0.794732    
## ethnic_groupgroup C:parent_educsome college                 0.376 0.707455    
## ethnic_groupgroup D:parent_educsome college                 1.331 0.183836    
## ethnic_groupgroup E:parent_educsome college                 0.200 0.841866    
## ethnic_groupgroup B:parent_educsome high school            -1.713 0.087450 .  
## ethnic_groupgroup C:parent_educsome high school            -0.598 0.550037    
## ethnic_groupgroup D:parent_educsome high school            -0.133 0.893944    
## ethnic_groupgroup E:parent_educsome high school             0.251 0.801944    
## ethnic_groupgroup B:lunch_typestandard                      0.638 0.523555    
## ethnic_groupgroup C:lunch_typestandard                      1.394 0.163987    
## ethnic_groupgroup D:lunch_typestandard                      0.797 0.426112    
## ethnic_groupgroup E:lunch_typestandard                      0.129 0.897536    
## ethnic_groupgroup B:test_prepnone                           0.404 0.686423    
## ethnic_groupgroup C:test_prepnone                           1.377 0.169289    
## ethnic_groupgroup D:test_prepnone                           1.375 0.169796    
## ethnic_groupgroup E:test_prepnone                           1.862 0.063307 .  
## ethnic_groupgroup B:parent_marital_statusmarried            0.553 0.580679    
## ethnic_groupgroup C:parent_marital_statusmarried            0.342 0.732511    
## ethnic_groupgroup D:parent_marital_statusmarried           -1.160 0.246704    
## ethnic_groupgroup E:parent_marital_statusmarried           -0.306 0.759941    
## ethnic_groupgroup B:parent_marital_statussingle             1.175 0.240572    
## ethnic_groupgroup C:parent_marital_statussingle             0.359 0.720004    
## ethnic_groupgroup D:parent_marital_statussingle            -0.264 0.791728    
## ethnic_groupgroup E:parent_marital_statussingle             0.601 0.548513    
## ethnic_groupgroup B:parent_marital_statuswidowed            1.041 0.298536    
## ethnic_groupgroup C:parent_marital_statuswidowed            1.640 0.101768    
## ethnic_groupgroup D:parent_marital_statuswidowed            0.358 0.720446    
## ethnic_groupgroup E:parent_marital_statuswidowed               NA       NA    
## ethnic_groupgroup B:practice_sportregularly                 1.682 0.093341 .  
## ethnic_groupgroup C:practice_sportregularly                 1.461 0.144908    
## ethnic_groupgroup D:practice_sportregularly                 1.315 0.189183    
## ethnic_groupgroup E:practice_sportregularly                 1.483 0.138959    
## ethnic_groupgroup B:practice_sportsometimes                 1.066 0.287304    
## ethnic_groupgroup C:practice_sportsometimes                 1.687 0.092504 .  
## ethnic_groupgroup D:practice_sportsometimes                 1.040 0.299174    
## ethnic_groupgroup E:practice_sportsometimes                 1.011 0.312443    
## ethnic_groupgroup B:is_first_childyes                       1.706 0.088779 .  
## ethnic_groupgroup C:is_first_childyes                      -0.032 0.974411    
## ethnic_groupgroup D:is_first_childyes                       0.199 0.842418    
## ethnic_groupgroup E:is_first_childyes                       0.543 0.587200    
## ethnic_groupgroup B:transport_meansschool_bus              -0.684 0.494241    
## ethnic_groupgroup C:transport_meansschool_bus              -1.837 0.066921 .  
## ethnic_groupgroup D:transport_meansschool_bus              -0.539 0.590297    
## ethnic_groupgroup E:transport_meansschool_bus              -1.804 0.072093 .  
## ethnic_groupgroup B:wkly_study_hours> 10                   -0.984 0.325710    
## ethnic_groupgroup C:wkly_study_hours> 10                    0.140 0.888562    
## ethnic_groupgroup D:wkly_study_hours> 10                    0.416 0.678007    
## ethnic_groupgroup E:wkly_study_hours> 10                   -0.319 0.749646    
## ethnic_groupgroup B:wkly_study_hours10-May                 -0.698 0.485813    
## ethnic_groupgroup C:wkly_study_hours10-May                  0.286 0.775035    
## ethnic_groupgroup D:wkly_study_hours10-May                  0.301 0.763685    
## ethnic_groupgroup E:wkly_study_hours10-May                 -0.290 0.772121    
## parent_educbachelor's degree:lunch_typestandard             0.411 0.681330    
## parent_educhigh school:lunch_typestandard                   0.089 0.929339    
## parent_educmaster's degree:lunch_typestandard               1.305 0.192749    
## parent_educsome college:lunch_typestandard                  0.790 0.430256    
## parent_educsome high school:lunch_typestandard              1.277 0.202472    
## parent_educbachelor's degree:test_prepnone                 -0.839 0.401869    
## parent_educhigh school:test_prepnone                       -0.260 0.794920    
## parent_educmaster's degree:test_prepnone                   -0.225 0.822173    
## parent_educsome college:test_prepnone                      -0.552 0.581102    
## parent_educsome high school:test_prepnone                   0.731 0.465380    
## parent_educbachelor's degree:parent_marital_statusmarried  -2.096 0.036705 *  
## parent_educhigh school:parent_marital_statusmarried         0.264 0.792052    
## parent_educmaster's degree:parent_marital_statusmarried     0.250 0.802627    
## parent_educsome college:parent_marital_statusmarried       -1.431 0.153379    
## parent_educsome high school:parent_marital_statusmarried   -1.355 0.176143    
## parent_educbachelor's degree:parent_marital_statussingle   -2.160 0.031431 *  
## parent_educhigh school:parent_marital_statussingle          0.615 0.539246    
## parent_educmaster's degree:parent_marital_statussingle     -0.187 0.851886    
## parent_educsome college:parent_marital_statussingle        -1.446 0.149058    
## parent_educsome high school:parent_marital_statussingle    -1.505 0.133023    
## parent_educbachelor's degree:parent_marital_statuswidowed  -0.432 0.666171    
## parent_educhigh school:parent_marital_statuswidowed        -1.193 0.233767    
## parent_educmaster's degree:parent_marital_statuswidowed    -2.133 0.033557 *  
## parent_educsome college:parent_marital_statuswidowed       -1.757 0.079672 .  
## parent_educsome high school:parent_marital_statuswidowed   -1.190 0.234766    
## parent_educbachelor's degree:practice_sportregularly       -0.426 0.670053    
## parent_educhigh school:practice_sportregularly             -1.813 0.070647 .  
## parent_educmaster's degree:practice_sportregularly          0.066 0.947437    
## parent_educsome college:practice_sportregularly            -0.028 0.977692    
## parent_educsome high school:practice_sportregularly        -0.377 0.706532    
## parent_educbachelor's degree:practice_sportsometimes       -1.480 0.139724    
## parent_educhigh school:practice_sportsometimes             -1.894 0.058951 .  
## parent_educmaster's degree:practice_sportsometimes          1.023 0.307081    
## parent_educsome college:practice_sportsometimes             0.173 0.862420    
## parent_educsome high school:practice_sportsometimes         0.063 0.949489    
## parent_educbachelor's degree:is_first_childyes              0.398 0.691162    
## parent_educhigh school:is_first_childyes                    1.943 0.052773 .  
## parent_educmaster's degree:is_first_childyes                0.873 0.383445    
## parent_educsome college:is_first_childyes                   2.128 0.033972 *  
## parent_educsome high school:is_first_childyes               1.067 0.286450    
## parent_educbachelor's degree:transport_meansschool_bus      1.047 0.295600    
## parent_educhigh school:transport_meansschool_bus            0.989 0.323307    
## parent_educmaster's degree:transport_meansschool_bus        1.831 0.067950 .  
## parent_educsome college:transport_meansschool_bus           1.163 0.245371    
## parent_educsome high school:transport_meansschool_bus       1.627 0.104635    
## parent_educbachelor's degree:wkly_study_hours> 10          -1.927 0.054721 .  
## parent_educhigh school:wkly_study_hours> 10                -1.591 0.112471    
## parent_educmaster's degree:wkly_study_hours> 10             0.462 0.644281    
## parent_educsome college:wkly_study_hours> 10               -1.132 0.258463    
## parent_educsome high school:wkly_study_hours> 10           -1.738 0.083002 .  
## parent_educbachelor's degree:wkly_study_hours10-May        -0.646 0.518891    
## parent_educhigh school:wkly_study_hours10-May              -1.948 0.052093 .  
## parent_educmaster's degree:wkly_study_hours10-May           0.139 0.889578    
## parent_educsome college:wkly_study_hours10-May             -0.704 0.481637    
## parent_educsome high school:wkly_study_hours10-May         -1.955 0.051251 .  
## lunch_typestandard:test_prepnone                           -0.625 0.532521    
## lunch_typestandard:parent_marital_statusmarried            -1.540 0.124305    
## lunch_typestandard:parent_marital_statussingle             -0.467 0.640946    
## lunch_typestandard:parent_marital_statuswidowed            -0.271 0.786200    
## lunch_typestandard:practice_sportregularly                  1.927 0.054686 .  
## lunch_typestandard:practice_sportsometimes                  2.131 0.033689 *  
## lunch_typestandard:is_first_childyes                        0.041 0.967588    
## lunch_typestandard:transport_meansschool_bus               -0.866 0.386933    
## lunch_typestandard:wkly_study_hours> 10                     1.299 0.194815    
## lunch_typestandard:wkly_study_hours10-May                   0.179 0.857717    
## test_prepnone:parent_marital_statusmarried                  1.363 0.173819    
## test_prepnone:parent_marital_statussingle                   0.533 0.594231    
## test_prepnone:parent_marital_statuswidowed                 -1.666 0.096615 .  
## test_prepnone:practice_sportregularly                       0.305 0.760155    
## test_prepnone:practice_sportsometimes                       0.623 0.533633    
## test_prepnone:is_first_childyes                            -0.215 0.829855    
## test_prepnone:transport_meansschool_bus                     0.146 0.884028    
## test_prepnone:wkly_study_hours> 10                         -1.053 0.292966    
## test_prepnone:wkly_study_hours10-May                        0.476 0.634185    
## parent_marital_statusmarried:practice_sportregularly        1.367 0.172546    
## parent_marital_statussingle:practice_sportregularly         0.300 0.764107    
## parent_marital_statuswidowed:practice_sportregularly        0.265 0.791500    
## parent_marital_statusmarried:practice_sportsometimes        0.778 0.436770    
## parent_marital_statussingle:practice_sportsometimes        -0.189 0.849955    
## parent_marital_statuswidowed:practice_sportsometimes           NA       NA    
## parent_marital_statusmarried:is_first_childyes             -2.604 0.009583 ** 
## parent_marital_statussingle:is_first_childyes              -0.911 0.363014    
## parent_marital_statuswidowed:is_first_childyes              1.582 0.114379    
## parent_marital_statusmarried:transport_meansschool_bus      1.142 0.254126    
## parent_marital_statussingle:transport_meansschool_bus      -0.439 0.660982    
## parent_marital_statuswidowed:transport_meansschool_bus     -1.735 0.083576 .  
## parent_marital_statusmarried:wkly_study_hours> 10           2.865 0.004403 ** 
## parent_marital_statussingle:wkly_study_hours> 10            3.102 0.002064 ** 
## parent_marital_statuswidowed:wkly_study_hours> 10              NA       NA    
## parent_marital_statusmarried:wkly_study_hours10-May         0.263 0.793062    
## parent_marital_statussingle:wkly_study_hours10-May          0.655 0.513103    
## parent_marital_statuswidowed:wkly_study_hours10-May            NA       NA    
## practice_sportregularly:is_first_childyes                  -0.550 0.582650    
## practice_sportsometimes:is_first_childyes                  -0.925 0.355759    
## practice_sportregularly:transport_meansschool_bus           1.985 0.047872 *  
## practice_sportsometimes:transport_meansschool_bus           1.227 0.220411    
## practice_sportregularly:wkly_study_hours> 10                0.368 0.712800    
## practice_sportsometimes:wkly_study_hours> 10                0.296 0.767511    
## practice_sportregularly:wkly_study_hours10-May              1.435 0.152043    
## practice_sportsometimes:wkly_study_hours10-May              0.477 0.633796    
## is_first_childyes:transport_meansschool_bus                -1.761 0.079028 .  
## is_first_childyes:wkly_study_hours> 10                      0.616 0.538468    
## is_first_childyes:wkly_study_hours10-May                   -1.429 0.153714    
## transport_meansschool_bus:wkly_study_hours> 10              0.912 0.362481    
## transport_meansschool_bus:wkly_study_hours10-May            0.874 0.382459    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 13.21 on 383 degrees of freedom
## Multiple R-squared:  0.5635, Adjusted R-squared:  0.3287 
## F-statistic:   2.4 on 206 and 383 DF,  p-value: 7.833e-14
stepwise_model_math <- step(full_fit_math, direction = "both", trace = 1)
## Start:  AIC=3204.25
## math_score ~ (gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours)^2
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:parent_educ               20    3316.3 70110 3192.8
## - parent_educ:test_prep                   5     440.1 67234 3198.1
## - gender:parent_marital_status            3      54.0 66847 3198.7
## - parent_educ:lunch_type                  5     591.2 67385 3199.4
## - ethnic_group:wkly_study_hours           8    1323.8 68117 3199.8
## - parent_educ:wkly_study_hours           10    1801.1 68595 3199.9
## - test_prep:practice_sport                2      93.5 66887 3201.1
## - parent_marital_status:practice_sport    4     550.9 67344 3201.1
## - gender:practice_sport                   2     107.4 66901 3201.2
## - gender:wkly_study_hours                 2     123.6 66917 3201.3
## - parent_educ:transport_means             5     809.3 67603 3201.4
## - ethnic_group:lunch_type                 4     591.0 67384 3201.4
## - transport_means:wkly_study_hours        2     187.6 66981 3201.9
## - practice_sport:is_first_child           2     198.4 66992 3202.0
## - lunch_type:is_first_child               1       0.3 66794 3202.3
## - gender:test_prep                        1       2.4 66796 3202.3
## - gender:transport_means                  1       3.3 66797 3202.3
## - test_prep:transport_means               1       3.7 66797 3202.3
## - test_prep:is_first_child                1       8.1 66802 3202.3
## - practice_sport:wkly_study_hours         4     718.0 67511 3202.6
## - lunch_type:test_prep                    1      68.1 66862 3202.9
## - ethnic_group:practice_sport             8    1701.9 68495 3203.1
## - lunch_type:wkly_study_hours             2     352.3 67146 3203.4
## - lunch_type:transport_means              1     130.8 66924 3203.4
## - gender:lunch_type                       1     135.1 66929 3203.4
## - gender:is_first_child                   1     148.7 66942 3203.6
## - test_prep:parent_marital_status         2     403.4 67197 3203.8
## - gender:ethnic_group                     4     869.6 67663 3203.9
## - parent_educ:is_first_child              5    1132.1 67926 3204.2
## <none>                                                66793 3204.3
## - gender:parent_educ                      5    1173.5 67967 3204.5
## - test_prep:wkly_study_hours              2     516.4 67310 3204.8
## - ethnic_group:parent_marital_status      9    2150.3 68944 3204.9
## - lunch_type:parent_marital_status        2     552.7 67346 3205.1
## - ethnic_group:test_prep                  4    1027.0 67820 3205.3
## - parent_educ:practice_sport             10    2545.2 69339 3206.3
## - ethnic_group:is_first_child             4    1194.4 67988 3206.7
## - parent_educ:parent_marital_status      13    3334.3 70128 3207.0
## - is_first_child:transport_means          1     540.9 67334 3207.0
## - practice_sport:transport_means          2     773.2 67567 3207.0
## - is_first_child:wkly_study_hours         2     781.2 67575 3207.1
## - lunch_type:practice_sport               2     806.9 67600 3207.3
## - ethnic_group:transport_means            4    1369.9 68163 3208.2
## - parent_marital_status:transport_means   3    1399.6 68193 3210.5
## - parent_marital_status:wkly_study_hours  4    2104.0 68897 3214.5
## - parent_marital_status:is_first_child    2    1736.9 68530 3215.4
## 
## Step:  AIC=3192.84
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     parent_educ:lunch_type + parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + parent_educ:wkly_study_hours + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:wkly_study_hours           10    1343.3 71453 3184.0
## - ethnic_group:wkly_study_hours           8     963.6 71073 3184.9
## - parent_educ:test_prep                   5     338.0 70448 3185.7
## - parent_educ:lunch_type                  5     451.8 70562 3186.6
## - gender:parent_marital_status            3      77.7 70187 3187.5
## - ethnic_group:practice_sport             8    1396.5 71506 3188.5
## - parent_marital_status:practice_sport    4     526.1 70636 3189.3
## - gender:wkly_study_hours                 2      84.8 70194 3189.6
## - test_prep:practice_sport                2      90.5 70200 3189.6
## - parent_educ:transport_means             5     905.7 71015 3190.4
## - practice_sport:is_first_child           2     203.1 70313 3190.5
## - ethnic_group:lunch_type                 4     690.5 70800 3190.6
## - gender:practice_sport                   2     238.2 70348 3190.8
## - lunch_type:is_first_child               1       0.2 70110 3190.8
## - gender:transport_means                  1       0.2 70110 3190.8
## - lunch_type:test_prep                    1       1.0 70111 3190.8
## - gender:test_prep                        1       6.0 70116 3190.9
## - test_prep:transport_means               1      13.7 70123 3191.0
## - gender:is_first_child                   1      26.2 70136 3191.1
## - test_prep:is_first_child                1      33.4 70143 3191.1
## - lunch_type:parent_marital_status        2     291.9 70402 3191.3
## - gender:lunch_type                       1     114.9 70225 3191.8
## - ethnic_group:test_prep                  4     836.4 70946 3191.8
## - transport_means:wkly_study_hours        2     360.6 70470 3191.9
## - practice_sport:wkly_study_hours         4     853.3 70963 3192.0
## - parent_educ:is_first_child              5    1098.4 71208 3192.0
## - gender:ethnic_group                     4     860.5 70970 3192.0
## - test_prep:parent_marital_status         2     402.3 70512 3192.2
## - gender:parent_educ                      5    1125.5 71235 3192.2
## - lunch_type:transport_means              1     226.0 70336 3192.7
## <none>                                                70110 3192.8
## - lunch_type:wkly_study_hours             2     538.0 70648 3193.3
## - is_first_child:wkly_study_hours         2     543.0 70653 3193.4
## - test_prep:wkly_study_hours              2     569.9 70680 3193.6
## - ethnic_group:parent_marital_status      9    2293.6 72403 3193.8
## - parent_educ:practice_sport             10    2568.4 72678 3194.1
## - is_first_child:transport_means          1     470.4 70580 3194.8
## - practice_sport:transport_means          2     724.0 70834 3194.9
## - lunch_type:practice_sport               2     860.0 70970 3196.0
## - ethnic_group:transport_means            4    1409.3 71519 3196.6
## - parent_marital_status:transport_means   3    1169.4 71279 3196.6
## - ethnic_group:is_first_child             4    1483.9 71594 3197.2
## - parent_marital_status:wkly_study_hours  4    1669.0 71779 3198.7
## - parent_educ:parent_marital_status      13    3948.0 74058 3199.2
## - parent_marital_status:is_first_child    2    1642.9 71753 3202.5
## + ethnic_group:parent_educ               20    3316.3 66793 3204.3
## 
## Step:  AIC=3184.04
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + ethnic_group:wkly_study_hours + 
##     parent_educ:lunch_type + parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:wkly_study_hours           8    1060.7 72514 3176.7
## - parent_educ:lunch_type                  5     330.0 71783 3176.8
## - parent_educ:test_prep                   5     395.5 71848 3177.3
## - gender:parent_marital_status            3      71.4 71524 3178.6
## - ethnic_group:practice_sport             8    1299.7 72753 3178.7
## - ethnic_group:lunch_type                 4     543.5 71997 3180.5
## - parent_marital_status:practice_sport    4     607.7 72061 3181.0
## - test_prep:practice_sport                2     164.8 71618 3181.4
## - gender:wkly_study_hours                 2     178.6 71632 3181.5
## - gender:practice_sport                   2     193.6 71647 3181.6
## - practice_sport:is_first_child           2     204.1 71657 3181.7
## - parent_educ:transport_means             5     939.1 72392 3181.7
## - practice_sport:wkly_study_hours         4     701.9 72155 3181.8
## - lunch_type:test_prep                    1       0.1 71453 3182.0
## - gender:transport_means                  1       2.0 71455 3182.1
## - lunch_type:is_first_child               1       7.3 71460 3182.1
## - gender:test_prep                        1       9.7 71463 3182.1
## - ethnic_group:test_prep                  4     740.2 72193 3182.1
## - test_prep:is_first_child                1      16.6 71470 3182.2
## - test_prep:transport_means               1      16.8 71470 3182.2
## - gender:is_first_child                   1      23.1 71476 3182.2
## - lunch_type:parent_marital_status        2     307.7 71761 3182.6
## - lunch_type:wkly_study_hours             2     327.7 71781 3182.7
## - gender:lunch_type                       1      94.3 71547 3182.8
## - gender:parent_educ                      5    1100.3 72553 3183.1
## - transport_means:wkly_study_hours        2     407.0 71860 3183.4
## - parent_educ:is_first_child              5    1144.4 72597 3183.4
## - is_first_child:wkly_study_hours         2     417.3 71870 3183.5
## - gender:ethnic_group                     4     920.2 72373 3183.6
## - test_prep:parent_marital_status         2     440.7 71894 3183.7
## <none>                                                71453 3184.0
## - lunch_type:transport_means              1     318.5 71772 3184.7
## - practice_sport:transport_means          2     638.5 72091 3185.3
## - is_first_child:transport_means          1     494.4 71947 3186.1
## - ethnic_group:parent_marital_status      9    2511.3 73964 3186.4
## - ethnic_group:transport_means            4    1268.3 72721 3186.4
## - lunch_type:practice_sport               2     795.8 72249 3186.6
## - test_prep:wkly_study_hours              2     800.9 72254 3186.6
## - parent_educ:practice_sport             10    2798.9 74252 3186.7
## - parent_marital_status:transport_means   3    1242.1 72695 3188.2
## - ethnic_group:is_first_child             4    1585.3 73038 3189.0
## - parent_marital_status:wkly_study_hours  4    1707.0 73160 3190.0
## - parent_educ:parent_marital_status      13    4246.1 75699 3192.1
## + parent_educ:wkly_study_hours           10    1343.3 70110 3192.8
## - parent_marital_status:is_first_child    2    1880.9 73334 3195.4
## + ethnic_group:parent_educ               20    2858.5 68595 3199.9
## 
## Step:  AIC=3176.73
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:lunch_type                  5     294.6 72808 3169.1
## - parent_educ:test_prep                   5     425.1 72939 3170.2
## - gender:parent_marital_status            3      77.7 72591 3171.4
## - ethnic_group:practice_sport             8    1324.8 73838 3171.4
## - parent_marital_status:practice_sport    4     477.7 72991 3172.6
## - ethnic_group:lunch_type                 4     592.3 73106 3173.5
## - parent_educ:transport_means             5     852.7 73366 3173.6
## - gender:wkly_study_hours                 2     138.0 72652 3173.9
## - test_prep:practice_sport                2     157.5 72671 3174.0
## - ethnic_group:test_prep                  4     699.6 73213 3174.4
## - gender:practice_sport                   2     212.8 72726 3174.5
## - practice_sport:wkly_study_hours         4     715.7 73229 3174.5
## - practice_sport:is_first_child           2     230.8 72744 3174.6
## - lunch_type:test_prep                    1       3.8 72518 3174.8
## - gender:transport_means                  1       3.8 72518 3174.8
## - transport_means:wkly_study_hours        2     251.7 72765 3174.8
## - gender:is_first_child                   1       9.8 72523 3174.8
## - lunch_type:is_first_child               1      10.0 72524 3174.8
## - test_prep:transport_means               1      14.0 72528 3174.8
## - gender:test_prep                        1      32.5 72546 3175.0
## - test_prep:is_first_child                1      49.0 72563 3175.1
## - gender:parent_educ                      5    1062.9 73577 3175.3
## - lunch_type:parent_marital_status        2     327.1 72841 3175.4
## - gender:lunch_type                       1     100.0 72614 3175.5
## - lunch_type:wkly_study_hours             2     408.7 72922 3176.0
## - gender:ethnic_group                     4     915.4 73429 3176.1
## - parent_educ:is_first_child              5    1198.1 73712 3176.4
## <none>                                                72514 3176.7
## - test_prep:parent_marital_status         2     499.2 73013 3176.8
## - is_first_child:wkly_study_hours         2     516.9 73031 3176.9
## - lunch_type:transport_means              1     292.6 72806 3177.1
## - ethnic_group:parent_marital_status      9    2400.6 74914 3177.9
## - practice_sport:transport_means          2     658.8 73173 3178.1
## - ethnic_group:transport_means            4    1211.0 73725 3178.5
## - parent_educ:practice_sport             10    2730.9 75245 3178.5
## - is_first_child:transport_means          1     494.6 73008 3178.7
## - test_prep:wkly_study_hours              2     797.9 73312 3179.2
## - lunch_type:practice_sport               2     872.4 73386 3179.8
## - parent_marital_status:transport_means   3    1276.5 73790 3181.0
## - parent_marital_status:wkly_study_hours  4    1550.3 74064 3181.2
## - ethnic_group:is_first_child             4    1638.0 74152 3181.9
## - parent_educ:parent_marital_status      13    4105.1 76619 3183.2
## + ethnic_group:wkly_study_hours           8    1060.7 71453 3184.0
## + parent_educ:wkly_study_hours           10    1440.4 71073 3184.9
## - parent_marital_status:is_first_child    2    1784.1 74298 3187.1
## + ethnic_group:parent_educ               20    2546.0 69968 3195.6
## 
## Step:  AIC=3169.12
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:test_prep                   5     359.4 73168 3162.0
## - ethnic_group:practice_sport             8    1287.1 74095 3163.5
## - gender:parent_marital_status            3      84.3 72893 3163.8
## - parent_marital_status:practice_sport    4     510.3 73319 3165.2
## - ethnic_group:lunch_type                 4     611.1 73419 3166.1
## - gender:wkly_study_hours                 2     132.3 72941 3166.2
## - test_prep:practice_sport                2     157.8 72966 3166.4
## - parent_educ:transport_means             5     914.4 73723 3166.5
## - ethnic_group:test_prep                  4     686.0 73494 3166.7
## - gender:practice_sport                   2     217.7 73026 3166.9
## - practice_sport:is_first_child           2     246.8 73055 3167.1
## - gender:transport_means                  1       1.0 72809 3167.1
## - lunch_type:test_prep                    1       1.8 72810 3167.1
## - test_prep:transport_means               1      14.7 72823 3167.2
## - lunch_type:is_first_child               1      14.9 72823 3167.2
## - practice_sport:wkly_study_hours         4     759.8 73568 3167.2
## - transport_means:wkly_study_hours        2     270.4 73079 3167.3
## - gender:is_first_child                   1      30.9 72839 3167.4
## - gender:test_prep                        1      38.9 72847 3167.4
## - test_prep:is_first_child                1      39.2 72847 3167.4
## - gender:parent_educ                      5    1056.1 73864 3167.6
## - lunch_type:parent_marital_status        2     329.5 73138 3167.8
## - lunch_type:wkly_study_hours             2     370.3 73179 3168.1
## - gender:lunch_type                       1     140.8 72949 3168.3
## - gender:ethnic_group                     4     914.4 73723 3168.5
## - parent_educ:is_first_child              5    1171.9 73980 3168.5
## <none>                                                72808 3169.1
## - test_prep:parent_marital_status         2     532.2 73340 3169.4
## - lunch_type:transport_means              1     287.4 73096 3169.4
## - is_first_child:wkly_study_hours         2     545.4 73354 3169.5
## - ethnic_group:parent_marital_status      9    2363.0 75171 3170.0
## - ethnic_group:transport_means            4    1190.2 73998 3170.7
## - practice_sport:transport_means          2     751.2 73559 3171.2
## - is_first_child:transport_means          1     510.9 73319 3171.2
## - test_prep:wkly_study_hours              2     786.4 73595 3171.5
## - lunch_type:practice_sport               2     835.6 73644 3171.9
## - parent_educ:practice_sport             10    2882.8 75691 3172.0
## - parent_marital_status:transport_means   3    1345.6 74154 3173.9
## - ethnic_group:is_first_child             4    1656.4 74465 3174.4
## - parent_marital_status:wkly_study_hours  4    1675.9 74484 3174.5
## - parent_educ:parent_marital_status      13    4184.5 76993 3176.1
## + parent_educ:lunch_type                  5     294.6 72514 3176.7
## + ethnic_group:wkly_study_hours           8    1025.2 71783 3176.8
## + parent_educ:wkly_study_hours           10    1298.6 71510 3178.5
## - parent_marital_status:is_first_child    2    1962.0 74770 3180.8
## + ethnic_group:parent_educ               20    2526.6 70282 3188.3
## 
## Step:  AIC=3162.03
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:practice_sport             8    1278.6 74446 3156.2
## - gender:parent_marital_status            3      87.6 73255 3156.7
## - parent_marital_status:practice_sport    4     490.9 73659 3158.0
## - ethnic_group:test_prep                  4     630.4 73798 3159.1
## - test_prep:practice_sport                2     132.4 73300 3159.1
## - gender:wkly_study_hours                 2     150.1 73318 3159.2
## - ethnic_group:lunch_type                 4     667.4 73835 3159.4
## - parent_educ:transport_means             5     964.9 74132 3159.8
## - gender:practice_sport                   2     214.9 73382 3159.8
## - gender:transport_means                  1       0.1 73168 3160.0
## - gender:parent_educ                      5    1000.6 74168 3160.0
## - practice_sport:wkly_study_hours         4     751.8 73919 3160.1
## - lunch_type:test_prep                    1       7.1 73175 3160.1
## - test_prep:transport_means               1      12.8 73180 3160.1
## - transport_means:wkly_study_hours        2     262.3 73430 3160.1
## - lunch_type:is_first_child               1      24.2 73192 3160.2
## - gender:is_first_child                   1      25.1 73193 3160.2
## - practice_sport:is_first_child           2     277.1 73445 3160.3
## - test_prep:is_first_child                1      46.8 73214 3160.4
## - gender:test_prep                        1      47.0 73215 3160.4
## - lunch_type:parent_marital_status        2     304.2 73472 3160.5
## - gender:lunch_type                       1     121.5 73289 3161.0
## - lunch_type:wkly_study_hours             2     410.5 73578 3161.3
## - gender:ethnic_group                     4     912.8 74080 3161.3
## - parent_educ:is_first_child              5    1196.4 74364 3161.6
## - is_first_child:wkly_study_hours         2     486.7 73654 3161.9
## <none>                                                73168 3162.0
## - lunch_type:transport_means              1     256.3 73424 3162.1
## - test_prep:parent_marital_status         2     519.3 73687 3162.2
## - ethnic_group:parent_marital_status      9    2307.6 75475 3162.3
## - ethnic_group:transport_means            4    1145.8 74313 3163.2
## - practice_sport:transport_means          2     780.1 73948 3164.3
## - parent_educ:practice_sport             10    2851.5 76019 3164.6
## - is_first_child:transport_means          1     590.4 73758 3164.8
## - test_prep:wkly_study_hours              2     856.9 74024 3164.9
## - lunch_type:practice_sport               2     894.2 74062 3165.2
## - parent_marital_status:transport_means   3    1347.2 74515 3166.8
## - parent_marital_status:wkly_study_hours  4    1749.0 74917 3168.0
## - ethnic_group:is_first_child             4    1750.8 74918 3168.0
## - parent_educ:parent_marital_status      13    4071.8 77239 3168.0
## + parent_educ:test_prep                   5     359.4 72808 3169.1
## + ethnic_group:wkly_study_hours           8    1054.8 72113 3169.5
## + parent_educ:lunch_type                  5     228.9 72939 3170.2
## + parent_educ:wkly_study_hours           10    1351.3 71816 3171.0
## - parent_marital_status:is_first_child    2    2006.6 75174 3174.0
## + ethnic_group:parent_educ               20    2379.5 70788 3182.5
## 
## Step:  AIC=3156.25
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:parent_marital_status            3      67.0 74513 3150.8
## - parent_educ:transport_means             5     841.7 75288 3152.9
## - test_prep:practice_sport                2     106.9 74553 3153.1
## - ethnic_group:test_prep                  4     620.2 75066 3153.1
## - gender:parent_educ                      5     928.1 75374 3153.6
## - parent_marital_status:practice_sport    4     715.9 75162 3153.9
## - gender:ethnic_group                     4     740.0 75186 3154.1
## - practice_sport:is_first_child           2     233.2 74679 3154.1
## - gender:wkly_study_hours                 2     239.5 74686 3154.1
## - ethnic_group:lunch_type                 4     753.4 75200 3154.2
## - practice_sport:wkly_study_hours         4     757.6 75204 3154.2
## - gender:transport_means                  1       0.0 74446 3154.2
## - gender:is_first_child                   1       4.0 74450 3154.3
## - lunch_type:is_first_child               1       6.3 74452 3154.3
## - test_prep:transport_means               1      14.3 74461 3154.4
## - gender:test_prep                        1      27.0 74473 3154.5
## - test_prep:is_first_child                1      36.1 74482 3154.5
## - lunch_type:test_prep                    1      40.4 74487 3154.6
## - transport_means:wkly_study_hours        2     312.2 74758 3154.7
## - lunch_type:parent_marital_status        2     336.7 74783 3154.9
## - gender:lunch_type                       1      91.8 74538 3155.0
## - gender:practice_sport                   2     372.3 74818 3155.2
## - lunch_type:wkly_study_hours             2     438.7 74885 3155.7
## - lunch_type:transport_means              1     207.5 74654 3155.9
## <none>                                                74446 3156.2
## - is_first_child:wkly_study_hours         2     513.1 74959 3156.3
## - test_prep:parent_marital_status         2     564.5 75011 3156.7
## - ethnic_group:parent_marital_status      9    2399.2 76845 3157.0
## - parent_educ:is_first_child              5    1373.5 75820 3157.0
## - test_prep:wkly_study_hours              2     686.9 75133 3157.7
## - ethnic_group:transport_means            4    1209.0 75655 3157.8
## - practice_sport:transport_means          2     767.5 75214 3158.3
## - lunch_type:practice_sport               2     901.2 75347 3159.3
## - parent_educ:practice_sport             10    2985.5 77432 3159.4
## - is_first_child:transport_means          1     699.2 75145 3159.8
## - ethnic_group:is_first_child             4    1570.1 76016 3160.6
## - parent_educ:parent_marital_status      13    4000.5 78447 3161.1
## - parent_marital_status:transport_means   3    1482.2 75928 3161.9
## + ethnic_group:practice_sport             8    1278.6 73168 3162.0
## - parent_marital_status:wkly_study_hours  4    1838.7 76285 3162.6
## + parent_educ:test_prep                   5     350.9 74095 3163.5
## + ethnic_group:wkly_study_hours           8    1066.6 73380 3163.7
## + parent_educ:lunch_type                  5     190.6 74256 3164.7
## + parent_educ:wkly_study_hours           10    1298.4 73148 3165.9
## - parent_marital_status:is_first_child    2    1757.2 76203 3166.0
## + ethnic_group:parent_educ               20    2053.9 72392 3179.7
## 
## Step:  AIC=3150.78
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:practice_sport + gender:is_first_child + gender:transport_means + 
##     gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:transport_means             5     837.2 75350 3147.4
## - test_prep:practice_sport                2     123.5 74637 3147.8
## - ethnic_group:test_prep                  4     647.9 75161 3147.9
## - gender:parent_educ                      5     953.7 75467 3148.3
## - parent_marital_status:practice_sport    4     707.6 75221 3148.4
## - gender:ethnic_group                     4     713.3 75227 3148.4
## - practice_sport:is_first_child           2     226.7 74740 3148.6
## - gender:transport_means                  1       0.1 74513 3148.8
## - ethnic_group:lunch_type                 4     763.7 75277 3148.8
## - lunch_type:is_first_child               1       5.5 74519 3148.8
## - gender:wkly_study_hours                 2     259.9 74773 3148.8
## - gender:is_first_child                   1       7.7 74521 3148.8
## - test_prep:transport_means               1      13.5 74527 3148.9
## - practice_sport:wkly_study_hours         4     781.9 75295 3148.9
## - gender:test_prep                        1      30.2 74543 3149.0
## - test_prep:is_first_child                1      37.1 74550 3149.1
## - lunch_type:test_prep                    1      38.2 74551 3149.1
## - transport_means:wkly_study_hours        2     313.8 74827 3149.3
## - gender:lunch_type                       1      86.4 74600 3149.5
## - lunch_type:parent_marital_status        2     372.7 74886 3149.7
## - gender:practice_sport                   2     398.1 74911 3149.9
## - lunch_type:wkly_study_hours             2     465.2 74978 3150.5
## - lunch_type:transport_means              1     219.7 74733 3150.5
## - is_first_child:wkly_study_hours         2     502.1 75015 3150.7
## <none>                                                74513 3150.8
## - test_prep:parent_marital_status         2     572.4 75086 3151.3
## - parent_educ:is_first_child              5    1383.9 75897 3151.6
## - test_prep:wkly_study_hours              2     682.1 75195 3152.2
## - ethnic_group:transport_means            4    1201.4 75715 3152.2
## - practice_sport:transport_means          2     757.6 75271 3152.7
## - ethnic_group:parent_marital_status      9    2645.4 77159 3153.4
## - lunch_type:practice_sport               2     979.2 75492 3154.5
## - parent_educ:practice_sport             10    3086.3 77599 3154.7
## - is_first_child:transport_means          1     756.1 75269 3154.7
## - ethnic_group:is_first_child             4    1552.8 76066 3154.9
## - parent_educ:parent_marital_status      13    3992.8 78506 3155.6
## + gender:parent_marital_status            3      67.0 74446 3156.2
## + ethnic_group:practice_sport             8    1258.0 73255 3156.7
## - parent_marital_status:wkly_study_hours  4    1820.1 76333 3157.0
## - parent_marital_status:transport_means   3    1677.8 76191 3157.9
## + parent_educ:test_prep                   5     353.8 74159 3158.0
## + ethnic_group:wkly_study_hours           8    1069.4 73444 3158.3
## + parent_educ:lunch_type                  5     197.6 74316 3159.2
## + parent_educ:wkly_study_hours           10    1285.8 73227 3160.5
## - parent_marital_status:is_first_child    2    1819.2 76332 3161.0
## + ethnic_group:parent_educ               20    2094.0 72419 3174.0
## 
## Step:  AIC=3147.37
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:practice_sport + gender:is_first_child + gender:transport_means + 
##     gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:ethnic_group                     4     625.0 75975 3144.2
## - parent_marital_status:practice_sport    4     639.9 75990 3144.4
## - test_prep:practice_sport                2     137.2 75488 3144.4
## - practice_sport:is_first_child           2     183.7 75534 3144.8
## - ethnic_group:test_prep                  4     699.4 76050 3144.8
## - gender:parent_educ                      5     964.7 76315 3144.9
## - gender:wkly_study_hours                 2     223.3 75574 3145.1
## - gender:transport_means                  1       0.0 75350 3145.4
## - lunch_type:is_first_child               1       3.2 75354 3145.4
## - gender:is_first_child                   1       3.4 75354 3145.4
## - test_prep:transport_means               1      18.3 75369 3145.5
## - gender:test_prep                        1      25.6 75376 3145.6
## - transport_means:wkly_study_hours        2     288.2 75639 3145.6
## - lunch_type:test_prep                    1      45.2 75396 3145.7
## - test_prep:is_first_child                1      70.8 75421 3145.9
## - practice_sport:wkly_study_hours         4     851.2 76202 3146.0
## - gender:lunch_type                       1     110.4 75461 3146.2
## - ethnic_group:lunch_type                 4     903.0 76253 3146.4
## - lunch_type:parent_marital_status        2     449.3 75800 3146.9
## - is_first_child:wkly_study_hours         2     475.6 75826 3147.1
## - lunch_type:transport_means              1     226.7 75577 3147.1
## - gender:practice_sport                   2     488.4 75839 3147.2
## <none>                                                75350 3147.4
## - test_prep:parent_marital_status         2     561.5 75912 3147.8
## - lunch_type:wkly_study_hours             2     588.6 75939 3148.0
## - practice_sport:transport_means          2     593.3 75944 3148.0
## - parent_educ:is_first_child              5    1426.3 76777 3148.4
## - test_prep:wkly_study_hours              2     674.7 76025 3148.6
## - ethnic_group:transport_means            4    1321.3 76672 3149.6
## - ethnic_group:parent_marital_status      9    2697.0 78047 3150.1
## - parent_educ:practice_sport             10    3037.1 78388 3150.7
## - is_first_child:transport_means          1     689.2 76040 3150.7
## + parent_educ:transport_means             5     837.2 74513 3150.8
## - ethnic_group:is_first_child             4    1647.5 76998 3152.1
## - lunch_type:practice_sport               2    1148.9 76499 3152.3
## - parent_educ:parent_marital_status      13    4056.5 79407 3152.3
## + gender:parent_marital_status            3      62.5 75288 3152.9
## - parent_marital_status:transport_means   3    1562.5 76913 3153.5
## - parent_marital_status:wkly_study_hours  4    1918.6 77269 3154.2
## + parent_educ:test_prep                   5     390.5 74960 3154.3
## + ethnic_group:practice_sport             8    1138.4 74212 3154.4
## + parent_educ:lunch_type                  5     246.2 75104 3155.4
## + ethnic_group:wkly_study_hours           8     977.8 74373 3155.7
## - parent_marital_status:is_first_child    2    1802.2 77153 3157.3
## + parent_educ:wkly_study_hours           10    1256.7 74094 3157.4
## + ethnic_group:parent_educ               20    2385.2 72965 3168.4
## 
## Step:  AIC=3144.24
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:parent_educ + 
##     gender:lunch_type + gender:test_prep + gender:practice_sport + 
##     gender:is_first_child + gender:transport_means + gender:wkly_study_hours + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:parent_educ                      5     803.3 76779 3140.5
## - ethnic_group:test_prep                  4     583.4 76559 3140.8
## - parent_marital_status:practice_sport    4     607.7 76583 3140.9
## - test_prep:practice_sport                2     130.4 76106 3141.3
## - practice_sport:is_first_child           2     230.6 76206 3142.0
## - gender:transport_means                  1       2.2 75978 3142.3
## - lunch_type:is_first_child               1       2.4 75978 3142.3
## - gender:is_first_child                   1       8.7 75984 3142.3
## - gender:test_prep                        1      14.5 75990 3142.4
## - test_prep:transport_means               1      15.5 75991 3142.4
## - gender:wkly_study_hours                 2     283.2 76259 3142.4
## - lunch_type:test_prep                    1      62.2 76038 3142.7
## - transport_means:wkly_study_hours        2     331.5 76307 3142.8
## - test_prep:is_first_child                1      78.2 76054 3142.9
## - gender:lunch_type                       1      98.6 76074 3143.0
## - practice_sport:wkly_study_hours         4     895.9 76871 3143.2
## - ethnic_group:lunch_type                 4     898.8 76874 3143.2
## - lunch_type:parent_marital_status        2     387.7 76363 3143.2
## - is_first_child:wkly_study_hours         2     485.3 76461 3144.0
## - lunch_type:transport_means              1     230.9 76206 3144.0
## - gender:practice_sport                   2     505.5 76481 3144.2
## <none>                                                75975 3144.2
## - test_prep:parent_marital_status         2     573.9 76549 3144.7
## - lunch_type:wkly_study_hours             2     580.0 76555 3144.7
## - practice_sport:transport_means          2     587.3 76563 3144.8
## - test_prep:wkly_study_hours              2     723.8 76699 3145.8
## - ethnic_group:parent_marital_status      9    2606.7 78582 3146.1
## - ethnic_group:transport_means            4    1335.3 77311 3146.5
## - parent_educ:is_first_child              5    1638.2 77614 3146.8
## + gender:ethnic_group                     4     625.0 75350 3147.4
## - parent_educ:practice_sport             10    3044.3 79020 3147.4
## - is_first_child:transport_means          1     745.1 76720 3148.0
## + parent_educ:transport_means             5     748.8 75227 3148.4
## - ethnic_group:is_first_child             4    1618.4 77594 3148.7
## - parent_educ:parent_marital_status      13    4147.5 80123 3149.6
## + gender:parent_marital_status            3      53.1 75922 3149.8
## - parent_marital_status:wkly_study_hours  4    1869.3 77845 3150.6
## - lunch_type:practice_sport               2    1362.2 77338 3150.7
## - parent_marital_status:transport_means   3    1625.8 77601 3150.7
## + parent_educ:test_prep                   5     378.4 75597 3151.3
## + parent_educ:lunch_type                  5     249.3 75726 3152.3
## + ethnic_group:practice_sport             8     990.4 74985 3152.5
## + ethnic_group:wkly_study_hours           8     951.0 75024 3152.8
## + parent_educ:wkly_study_hours           10    1276.1 74699 3154.3
## - parent_marital_status:is_first_child    2    1937.3 77913 3155.1
## + ethnic_group:parent_educ               20    2426.2 73549 3165.1
## 
## Step:  AIC=3140.45
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:test_prep                  4     579.8 77359 3136.9
## - parent_marital_status:practice_sport    4     610.1 77389 3137.1
## - test_prep:practice_sport                2     174.1 76953 3137.8
## - gender:transport_means                  1       2.3 76781 3138.5
## - lunch_type:is_first_child               1       3.9 76783 3138.5
## - gender:is_first_child                   1       8.2 76787 3138.5
## - ethnic_group:lunch_type                 4     793.2 77572 3138.5
## - test_prep:transport_means               1       8.6 76787 3138.5
## - practice_sport:is_first_child           2     271.5 77050 3138.5
## - gender:test_prep                        1      13.6 76792 3138.6
## - gender:wkly_study_hours                 2     305.8 77084 3138.8
## - transport_means:wkly_study_hours        2     333.7 77112 3139.0
## - practice_sport:wkly_study_hours         4     866.5 77645 3139.1
## - lunch_type:test_prep                    1      89.9 76869 3139.1
## - lunch_type:parent_marital_status        2     356.6 77135 3139.2
## - gender:lunch_type                       1     106.1 76885 3139.3
## - test_prep:is_first_child                1     121.6 76900 3139.4
## - gender:practice_sport                   2     513.8 77292 3140.4
## <none>                                                76779 3140.4
## - test_prep:parent_marital_status         2     543.9 77323 3140.6
## - is_first_child:wkly_study_hours         2     547.5 77326 3140.6
## - practice_sport:transport_means          2     576.1 77355 3140.9
## - lunch_type:transport_means              1     337.5 77116 3141.0
## - lunch_type:wkly_study_hours             2     602.4 77381 3141.1
## - ethnic_group:parent_marital_status      9    2495.1 79274 3141.3
## - parent_educ:is_first_child              5    1473.0 78252 3141.7
## - test_prep:wkly_study_hours              2     793.8 77573 3142.5
## - parent_educ:practice_sport             10    2997.2 79776 3143.0
## - ethnic_group:transport_means            4    1487.1 78266 3143.8
## - is_first_child:transport_means          1     729.0 77508 3144.0
## + gender:parent_educ                      5     803.3 75975 3144.2
## - ethnic_group:is_first_child             4    1574.1 78353 3144.4
## + parent_educ:transport_means             5     771.5 76007 3144.5
## + gender:ethnic_group                     4     463.6 76315 3144.9
## + gender:parent_marital_status            3      49.7 76729 3146.1
## - lunch_type:practice_sport               2    1378.5 78157 3146.9
## - parent_marital_status:wkly_study_hours  4    1932.2 78711 3147.1
## - parent_marital_status:transport_means   3    1712.3 78491 3147.5
## + parent_educ:test_prep                   5     325.1 76454 3147.9
## + parent_educ:lunch_type                  5     253.8 76525 3148.5
## - parent_educ:parent_marital_status      13    4591.9 81371 3148.7
## + ethnic_group:practice_sport             8     953.6 75825 3149.1
## + ethnic_group:wkly_study_hours           8     934.0 75845 3149.2
## + parent_educ:wkly_study_hours           10    1262.9 75516 3150.7
## - parent_marital_status:is_first_child    2    1915.9 78695 3151.0
## + ethnic_group:parent_educ               20    2444.2 74335 3161.4
## 
## Step:  AIC=3136.89
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_marital_status:practice_sport    4     533.2 77892 3132.9
## - test_prep:practice_sport                2     161.1 77520 3134.1
## - ethnic_group:lunch_type                 4     747.4 78106 3134.6
## - gender:transport_means                  1       1.4 77360 3134.9
## - gender:is_first_child                   1       3.8 77362 3134.9
## - lunch_type:is_first_child               1       8.7 77367 3135.0
## - gender:test_prep                        1      10.2 77369 3135.0
## - test_prep:transport_means               1      11.0 77370 3135.0
## - gender:wkly_study_hours                 2     274.9 77633 3135.0
## - practice_sport:is_first_child           2     307.1 77666 3135.2
## - practice_sport:wkly_study_hours         4     846.0 78204 3135.3
## - transport_means:wkly_study_hours        2     321.1 77680 3135.3
## - lunch_type:test_prep                    1      90.8 77449 3135.6
## - lunch_type:parent_marital_status        2     359.1 77718 3135.6
## - gender:lunch_type                       1      96.6 77455 3135.6
## - test_prep:is_first_child                1     102.3 77461 3135.7
## - test_prep:parent_marital_status         2     465.8 77824 3136.4
## - gender:practice_sport                   2     500.6 77859 3136.7
## - is_first_child:wkly_study_hours         2     507.8 77866 3136.8
## <none>                                                77359 3136.9
## - ethnic_group:parent_marital_status      9    2421.8 79780 3137.1
## - practice_sport:transport_means          2     583.7 77942 3137.3
## - lunch_type:transport_means              1     352.8 77711 3137.6
## - lunch_type:wkly_study_hours             2     639.5 77998 3137.8
## - parent_educ:is_first_child              5    1498.7 78857 3138.2
## - parent_educ:practice_sport             10    3002.3 80361 3139.3
## - test_prep:wkly_study_hours              2     860.1 78219 3139.4
## - is_first_child:transport_means          1     727.5 78086 3140.4
## + ethnic_group:test_prep                  4     579.8 76779 3140.4
## + parent_educ:transport_means             5     819.8 76539 3140.6
## + gender:parent_educ                      5     799.7 76559 3140.8
## - ethnic_group:is_first_child             4    1599.6 78958 3141.0
## - ethnic_group:transport_means            4    1611.9 78970 3141.1
## + gender:ethnic_group                     4     374.8 76984 3142.0
## + gender:parent_marital_status            3      72.6 77286 3142.3
## - parent_marital_status:wkly_study_hours  4    1929.3 79288 3143.4
## - lunch_type:practice_sport               2    1417.0 78776 3143.6
## - parent_marital_status:transport_means   3    1711.0 79070 3143.8
## + parent_educ:test_prep                   5     315.5 77043 3144.5
## + parent_educ:lunch_type                  5     243.5 77115 3145.0
## - parent_educ:parent_marital_status      13    4692.5 82051 3145.6
## + ethnic_group:practice_sport             8     942.1 76416 3145.7
## + ethnic_group:wkly_study_hours           8     878.6 76480 3146.2
## + parent_educ:wkly_study_hours           10    1190.6 76168 3147.7
## - parent_marital_status:is_first_child    2    2031.7 79390 3148.2
## + ethnic_group:parent_educ               20    2464.6 74894 3157.8
## 
## Step:  AIC=3132.94
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:parent_marital_status        3     368.2 78260 3129.7
## - test_prep:practice_sport                2     150.3 78042 3130.1
## - ethnic_group:lunch_type                 4     775.5 78667 3130.8
## - practice_sport:is_first_child           2     265.2 78157 3130.9
## - gender:is_first_child                   1       1.6 77893 3130.9
## - gender:transport_means                  1       3.6 77895 3131.0
## - test_prep:transport_means               1       9.1 77901 3131.0
## - lunch_type:is_first_child               1      14.4 77906 3131.1
## - gender:test_prep                        1      22.0 77914 3131.1
## - gender:wkly_study_hours                 2     316.5 78208 3131.3
## - transport_means:wkly_study_hours        2     323.4 78215 3131.4
## - ethnic_group:parent_marital_status     10    2477.6 80369 3131.4
## - practice_sport:wkly_study_hours         4     878.9 78771 3131.6
## - test_prep:is_first_child                1      96.0 77988 3131.7
## - lunch_type:test_prep                    1     100.7 77992 3131.7
## - gender:lunch_type                       1     110.2 78002 3131.8
## - test_prep:parent_marital_status         2     413.7 78305 3132.1
## - is_first_child:wkly_study_hours         2     514.9 78407 3132.8
## - gender:practice_sport                   2     523.4 78415 3132.9
## <none>                                                77892 3132.9
## - practice_sport:transport_means          2     544.8 78437 3133.1
## - lunch_type:transport_means              1     315.9 78208 3133.3
## - lunch_type:wkly_study_hours             2     646.8 78539 3133.8
## - parent_educ:is_first_child              5    1450.7 79342 3133.8
## - parent_educ:practice_sport             10    2867.2 80759 3134.3
## - ethnic_group:transport_means            4    1416.9 79309 3135.6
## - test_prep:wkly_study_hours              2     963.4 78855 3136.2
## - is_first_child:transport_means          1     722.5 78614 3136.4
## + parent_marital_status:practice_sport    4     533.2 77359 3136.9
## + gender:parent_educ                      5     794.5 77097 3136.9
## - ethnic_group:is_first_child             4    1601.7 79493 3136.9
## + parent_educ:transport_means             5     772.0 77120 3137.1
## + ethnic_group:test_prep                  4     502.9 77389 3137.1
## - parent_marital_status:wkly_study_hours  5    1966.9 79859 3137.7
## + gender:ethnic_group                     4     347.9 77544 3138.3
## + gender:parent_marital_status            3      64.2 77828 3138.5
## - parent_marital_status:transport_means   3    1696.1 79588 3139.7
## - lunch_type:practice_sport               2    1453.7 79345 3139.8
## + parent_educ:test_prep                   5     317.5 77574 3140.5
## + ethnic_group:practice_sport             8    1088.4 76803 3140.6
## + parent_educ:lunch_type                  5     251.8 77640 3141.0
## + ethnic_group:wkly_study_hours           8     797.6 77094 3142.9
## - parent_educ:parent_marital_status      14    5190.5 83082 3143.0
## + parent_educ:wkly_study_hours           10    1174.0 76718 3144.0
## - parent_marital_status:is_first_child    2    2196.3 80088 3145.3
## + ethnic_group:parent_educ               20    2483.8 75408 3153.8
## 
## Step:  AIC=3129.72
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:practice_sport                2     165.1 78425 3127.0
## - practice_sport:is_first_child           2     212.2 78472 3127.3
## - ethnic_group:lunch_type                 4     777.4 79037 3127.6
## - gender:is_first_child                   1       4.9 78265 3127.8
## - gender:wkly_study_hours                 2     271.6 78532 3127.8
## - gender:transport_means                  1       6.8 78267 3127.8
## - test_prep:transport_means               1      10.2 78270 3127.8
## - ethnic_group:parent_marital_status     10    2435.5 80696 3127.8
## - lunch_type:is_first_child               1      18.4 78278 3127.9
## - practice_sport:wkly_study_hours         4     826.1 79086 3127.9
## - gender:test_prep                        1      38.7 78299 3128.0
## - lunch_type:test_prep                    1      84.5 78345 3128.4
## - test_prep:is_first_child                1      94.7 78355 3128.4
## - transport_means:wkly_study_hours        2     361.1 78621 3128.4
## - test_prep:parent_marital_status         2     404.9 78665 3128.8
## - gender:lunch_type                       1     155.7 78416 3128.9
## - gender:practice_sport                   2     481.8 78742 3129.3
## - is_first_child:wkly_study_hours         2     484.9 78745 3129.4
## <none>                                                78260 3129.7
## - practice_sport:transport_means          2     535.6 78796 3129.8
## - lunch_type:transport_means              1     321.4 78581 3130.1
## - parent_educ:is_first_child              5    1397.5 79657 3130.2
## - lunch_type:wkly_study_hours             2     592.2 78852 3130.2
## - parent_educ:practice_sport             10    2842.9 81103 3130.8
## - ethnic_group:transport_means            4    1371.7 79632 3132.0
## - test_prep:wkly_study_hours              2     944.1 79204 3132.8
## + lunch_type:parent_marital_status        3     368.2 77892 3132.9
## - is_first_child:transport_means          1     745.6 79006 3133.3
## + parent_educ:transport_means             5     837.1 77423 3133.4
## - ethnic_group:is_first_child             4    1603.9 79864 3133.7
## + ethnic_group:test_prep                  4     514.1 77746 3133.8
## + gender:parent_educ                      5     758.5 77501 3134.0
## - parent_marital_status:wkly_study_hours  5    1918.3 80178 3134.0
## + gender:parent_marital_status            3      93.8 78166 3135.0
## + gender:ethnic_group                     4     302.8 77957 3135.4
## + parent_marital_status:practice_sport    5     542.4 77718 3135.6
## - lunch_type:practice_sport               2    1379.3 79639 3136.0
## - parent_marital_status:transport_means   3    1664.3 79924 3136.1
## + parent_educ:test_prep                   5     319.0 77941 3137.3
## + ethnic_group:practice_sport             8    1103.5 77156 3137.3
## + parent_educ:lunch_type                  5     272.2 77988 3137.7
## + ethnic_group:wkly_study_hours           8     800.2 77460 3139.7
## + parent_educ:wkly_study_hours           10    1154.0 77106 3141.0
## - parent_marital_status:is_first_child    2    2180.7 80441 3141.9
## - parent_educ:parent_marital_status      14    5685.1 83945 3143.1
## + ethnic_group:parent_educ               20    2274.4 75986 3152.3
## 
## Step:  AIC=3126.97
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:parent_marital_status + test_prep:is_first_child + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:parent_marital_status     10    2362.3 80787 3124.5
## - practice_sport:is_first_child           2     234.6 78660 3124.7
## - gender:wkly_study_hours                 2     257.8 78683 3124.9
## - gender:is_first_child                   1       2.9 78428 3125.0
## - gender:transport_means                  1       6.5 78432 3125.0
## - test_prep:transport_means               1      14.0 78439 3125.1
## - lunch_type:is_first_child               1      17.1 78442 3125.1
## - ethnic_group:lunch_type                 4     837.1 79262 3125.2
## - gender:test_prep                        1      37.2 78462 3125.2
## - practice_sport:wkly_study_hours         4     865.2 79290 3125.4
## - lunch_type:test_prep                    1      92.0 78517 3125.7
## - test_prep:is_first_child                1      99.3 78524 3125.7
## - transport_means:wkly_study_hours        2     387.2 78812 3125.9
## - gender:lunch_type                       1     168.8 78594 3126.2
## - test_prep:parent_marital_status         2     444.0 78869 3126.3
## - is_first_child:wkly_study_hours         2     453.2 78878 3126.4
## - practice_sport:transport_means          2     506.4 78931 3126.8
## - gender:practice_sport                   2     509.9 78935 3126.8
## <none>                                                78425 3127.0
## - lunch_type:transport_means              1     319.5 78745 3127.4
## - lunch_type:wkly_study_hours             2     643.8 79069 3127.8
## - parent_educ:practice_sport             10    2891.2 81316 3128.3
## - parent_educ:is_first_child              5    1540.6 79966 3128.4
## - ethnic_group:transport_means            4    1350.2 79775 3129.0
## + test_prep:practice_sport                2     165.1 78260 3129.7
## + lunch_type:parent_marital_status        3     383.1 78042 3130.1
## - test_prep:wkly_study_hours              2     952.3 79377 3130.1
## + parent_educ:transport_means             5     852.2 77573 3130.5
## - is_first_child:transport_means          1     755.8 79181 3130.6
## + gender:parent_educ                      5     805.0 77620 3130.9
## - parent_marital_status:wkly_study_hours  5    1874.3 80299 3130.9
## - ethnic_group:is_first_child             4    1614.4 80040 3131.0
## + ethnic_group:test_prep                  4     497.3 77928 3131.2
## + gender:parent_marital_status            3     119.3 78306 3132.1
## + gender:ethnic_group                     4     285.5 78140 3132.8
## + parent_marital_status:practice_sport    5     529.7 77895 3133.0
## - parent_marital_status:transport_means   3    1654.2 80079 3133.3
## - lunch_type:practice_sport               2    1438.7 79864 3133.7
## + parent_educ:test_prep                   5     295.7 78129 3134.7
## + ethnic_group:practice_sport             8    1085.0 77340 3134.8
## + parent_educ:lunch_type                  5     267.4 78158 3134.9
## + ethnic_group:wkly_study_hours           8     780.9 77644 3137.1
## + parent_educ:wkly_study_hours           10    1191.5 77234 3137.9
## - parent_marital_status:is_first_child    2    2135.4 80561 3138.8
## - parent_educ:parent_marital_status      14    5615.3 84040 3139.8
## + ethnic_group:parent_educ               20    2354.4 76071 3149.0
## 
## Step:  AIC=3124.48
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - practice_sport:is_first_child           2     134.9 80922 3121.5
## - practice_sport:wkly_study_hours         4     706.5 81494 3121.6
## - gender:wkly_study_hours                 2     192.1 80980 3121.9
## - transport_means:wkly_study_hours        2     268.3 81056 3122.4
## - practice_sport:transport_means          2     270.0 81057 3122.4
## - test_prep:parent_marital_status         3     558.2 81346 3122.5
## - test_prep:transport_means               1      12.1 80800 3122.6
## - gender:is_first_child                   1      21.6 80809 3122.6
## - gender:transport_means                  1      26.2 80814 3122.7
## - lunch_type:is_first_child               1      35.8 80823 3122.7
## - ethnic_group:lunch_type                 4     873.8 81661 3122.8
## - parent_educ:practice_sport             10    2583.4 83371 3123.1
## - lunch_type:test_prep                    1      87.2 80875 3123.1
## - gender:test_prep                        1      91.6 80879 3123.2
## - test_prep:is_first_child                1     138.6 80926 3123.5
## - is_first_child:wkly_study_hours         2     434.4 81222 3123.6
## - gender:lunch_type                       1     177.5 80965 3123.8
## - gender:practice_sport                   2     524.9 81312 3124.3
## <none>                                                80787 3124.5
## - lunch_type:wkly_study_hours             2     609.6 81397 3124.9
## - parent_marital_status:wkly_study_hours  6    1735.4 82523 3125.0
## - lunch_type:transport_means              1     384.1 81172 3125.3
## - ethnic_group:is_first_child             4    1283.6 82071 3125.8
## - ethnic_group:transport_means            4    1329.1 82117 3126.1
## - parent_educ:is_first_child              5    1623.5 82411 3126.2
## + ethnic_group:parent_marital_status     10    2362.3 78425 3127.0
## + gender:parent_marital_status            3     436.1 80351 3127.3
## - parent_marital_status:transport_means   3    1233.0 82020 3127.4
## + parent_educ:transport_means             5     917.7 79870 3127.7
## + test_prep:practice_sport                2      91.9 80696 3127.8
## + lunch_type:parent_marital_status        3     338.3 80449 3128.0
## - test_prep:wkly_study_hours              2    1155.0 81942 3128.8
## + ethnic_group:test_prep                  4     446.8 80341 3129.2
## + gender:parent_educ                      5     707.0 80080 3129.3
## - is_first_child:transport_means          1     981.3 81769 3129.6
## + gender:ethnic_group                     4     243.7 80544 3130.7
## + parent_marital_status:practice_sport    6     627.4 80160 3131.9
## - lunch_type:practice_sport               2    1582.8 82370 3131.9
## + parent_educ:test_prep                   5     304.0 80483 3132.2
## + parent_educ:lunch_type                  5     266.7 80521 3132.5
## + ethnic_group:practice_sport             8    1071.0 79716 3132.6
## - parent_marital_status:is_first_child    3    2014.8 82802 3133.0
## - parent_educ:parent_marital_status      15    5583.0 86370 3133.9
## + parent_educ:wkly_study_hours           10    1312.1 79475 3134.8
## + ethnic_group:wkly_study_hours           8     702.7 80085 3135.3
## + ethnic_group:parent_educ               20    2394.3 78393 3146.7
## 
## Step:  AIC=3121.46
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - practice_sport:wkly_study_hours         4     746.1 81668 3118.9
## - gender:wkly_study_hours                 2     197.4 81120 3118.9
## - practice_sport:transport_means          2     256.1 81178 3119.3
## - test_prep:parent_marital_status         3     542.8 81465 3119.4
## - transport_means:wkly_study_hours        2     274.7 81197 3119.5
## - test_prep:transport_means               1      12.3 80935 3119.6
## - gender:is_first_child                   1      25.8 80948 3119.7
## - lunch_type:is_first_child               1      27.4 80950 3119.7
## - gender:transport_means                  1      32.3 80955 3119.7
## - parent_educ:practice_sport             10    2575.3 83498 3119.9
## - ethnic_group:lunch_type                 4     901.1 81823 3120.0
## - lunch_type:test_prep                    1      98.2 81021 3120.2
## - gender:test_prep                        1     100.2 81023 3120.2
## - test_prep:is_first_child                1     105.9 81028 3120.2
## - is_first_child:wkly_study_hours         2     409.4 81332 3120.4
## - gender:lunch_type                       1     186.1 81108 3120.8
## - gender:practice_sport                   2     520.7 81443 3121.2
## <none>                                                80922 3121.5
## - lunch_type:wkly_study_hours             2     614.4 81537 3121.9
## - parent_marital_status:wkly_study_hours  6    1743.9 82666 3122.0
## - lunch_type:transport_means              1     376.8 81299 3122.2
## - ethnic_group:transport_means            4    1280.0 82202 3122.7
## - parent_educ:is_first_child              5    1598.0 82520 3123.0
## - ethnic_group:is_first_child             4    1368.9 82291 3123.4
## - parent_marital_status:transport_means   3    1178.7 82101 3124.0
## + gender:parent_marital_status            3     414.4 80508 3124.4
## + practice_sport:is_first_child           2     134.9 80787 3124.5
## + test_prep:practice_sport                2     104.1 80818 3124.7
## + ethnic_group:parent_marital_status     10    2262.6 78660 3124.7
## + parent_educ:transport_means             5     873.3 80049 3125.1
## + lunch_type:parent_marital_status        3     286.4 80636 3125.4
## - test_prep:wkly_study_hours              2    1121.2 82044 3125.6
## + ethnic_group:test_prep                  4     475.9 80446 3126.0
## + gender:parent_educ                      5     724.6 80198 3126.2
## - is_first_child:transport_means          1    1054.5 81977 3127.1
## + gender:ethnic_group                     4     280.3 80642 3127.4
## - lunch_type:practice_sport               2    1568.5 82491 3128.8
## + parent_educ:test_prep                   5     352.1 80570 3128.9
## + parent_educ:lunch_type                  5     272.5 80650 3129.5
## + parent_marital_status:practice_sport    6     543.3 80379 3129.5
## - parent_marital_status:is_first_child    3    1952.1 82874 3129.5
## + ethnic_group:practice_sport             8    1035.2 79887 3129.9
## - parent_educ:parent_marital_status      15    5525.4 86448 3130.4
## + parent_educ:wkly_study_hours           10    1304.2 79618 3131.9
## + ethnic_group:wkly_study_hours           8     727.5 80195 3132.1
## + ethnic_group:parent_educ               20    2361.2 78561 3144.0
## 
## Step:  AIC=3118.88
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:wkly_study_hours                 2     179.7 81848 3116.2
## - practice_sport:transport_means          2     229.3 81898 3116.5
## - ethnic_group:lunch_type                 4     793.3 82462 3116.6
## - test_prep:parent_marital_status         3     560.0 82228 3116.9
## - test_prep:transport_means               1      11.3 81680 3117.0
## - gender:transport_means                  1      15.7 81684 3117.0
## - transport_means:wkly_study_hours        2     295.9 81964 3117.0
## - parent_educ:practice_sport             10    2564.2 84233 3117.1
## - gender:is_first_child                   1      44.9 81713 3117.2
## - lunch_type:is_first_child               1      69.4 81738 3117.4
## - gender:test_prep                        1      88.2 81757 3117.5
## - lunch_type:test_prep                    1     131.6 81800 3117.8
## - test_prep:is_first_child                1     135.8 81804 3117.9
## - gender:lunch_type                       1     202.3 81871 3118.3
## - is_first_child:wkly_study_hours         2     498.4 82167 3118.5
## <none>                                                81668 3118.9
## - lunch_type:wkly_study_hours             2     556.9 82225 3118.9
## - gender:practice_sport                   2     560.6 82229 3118.9
## - lunch_type:transport_means              1     336.4 82005 3119.3
## - parent_educ:is_first_child              5    1501.0 83169 3119.6
## - parent_marital_status:wkly_study_hours  6    1807.4 83476 3119.8
## - ethnic_group:transport_means            4    1251.4 82920 3119.8
## - ethnic_group:is_first_child             4    1415.5 83084 3121.0
## + practice_sport:wkly_study_hours         4     746.1 80922 3121.5
## + practice_sport:is_first_child           2     174.5 81494 3121.6
## - parent_marital_status:transport_means   3    1236.0 82904 3121.7
## + test_prep:practice_sport                2     136.1 81532 3121.9
## + gender:parent_marital_status            3     401.9 81267 3122.0
## + parent_educ:transport_means             5     945.4 80723 3122.0
## + lunch_type:parent_marital_status        3     219.3 81449 3123.3
## - test_prep:wkly_study_hours              2    1185.6 82854 3123.4
## + ethnic_group:test_prep                  4     471.0 81197 3123.5
## + ethnic_group:parent_marital_status     10    2103.1 79565 3123.5
## + gender:parent_educ                      5     705.1 80963 3123.8
## + gender:ethnic_group                     4     333.0 81335 3124.5
## - is_first_child:transport_means          1    1069.1 82737 3124.6
## - lunch_type:practice_sport               2    1506.1 83174 3125.7
## + parent_educ:test_prep                   5     375.4 81293 3126.2
## + parent_educ:lunch_type                  5     326.2 81342 3126.5
## - parent_educ:parent_marital_status      15    5411.4 87080 3126.7
## - parent_marital_status:is_first_child    3    1942.8 83611 3126.8
## + parent_marital_status:practice_sport    6     469.0 81199 3127.5
## + ethnic_group:practice_sport             8     969.6 80699 3127.8
## + ethnic_group:wkly_study_hours           8     807.6 80861 3129.0
## + parent_educ:wkly_study_hours           10    1140.4 80528 3130.6
## + ethnic_group:parent_educ               20    2482.9 79186 3140.7
## 
## Step:  AIC=3116.17
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + ethnic_group:lunch_type + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:parent_marital_status + test_prep:is_first_child + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:lunch_type                 4     791.6 82640 3113.8
## - practice_sport:transport_means          2     245.4 82094 3113.9
## - test_prep:parent_marital_status         3     545.1 82393 3114.1
## - test_prep:transport_means               1      11.0 81859 3114.2
## - transport_means:wkly_study_hours        2     290.0 82138 3114.3
## - gender:transport_means                  1      18.5 81867 3114.3
## - parent_educ:practice_sport             10    2558.1 84406 3114.3
## - gender:is_first_child                   1      48.8 81897 3114.5
## - lunch_type:is_first_child               1      68.8 81917 3114.7
## - gender:test_prep                        1     110.7 81959 3115.0
## - lunch_type:test_prep                    1     122.5 81971 3115.1
## - test_prep:is_first_child                1     162.3 82010 3115.3
## - gender:lunch_type                       1     171.5 82020 3115.4
## - is_first_child:wkly_study_hours         2     495.3 82343 3115.7
## - lunch_type:wkly_study_hours             2     509.0 82357 3115.8
## <none>                                                81848 3116.2
## - gender:practice_sport                   2     570.2 82418 3116.3
## - lunch_type:transport_means              1     328.3 82176 3116.5
## - parent_educ:is_first_child              5    1504.7 83353 3116.9
## - ethnic_group:transport_means            4    1252.8 83101 3117.1
## - ethnic_group:is_first_child             4    1338.1 83186 3117.7
## - parent_marital_status:wkly_study_hours  6    2060.0 83908 3118.8
## + practice_sport:is_first_child           2     182.7 81665 3118.9
## + gender:wkly_study_hours                 2     179.7 81668 3118.9
## - parent_marital_status:transport_means   3    1218.2 83066 3118.9
## + practice_sport:wkly_study_hours         4     728.4 81120 3118.9
## + test_prep:practice_sport                2     138.9 81709 3119.2
## + gender:parent_marital_status            3     407.2 81441 3119.2
## + parent_educ:transport_means             5     888.5 80960 3119.7
## - test_prep:wkly_study_hours              2    1175.5 83024 3120.6
## + lunch_type:parent_marital_status        3     191.5 81657 3120.8
## + gender:parent_educ                      5     730.7 81117 3120.9
## + ethnic_group:test_prep                  4     436.0 81412 3121.0
## + ethnic_group:parent_marital_status     10    2063.5 79785 3121.1
## - is_first_child:transport_means          1    1003.7 82852 3121.4
## + gender:ethnic_group                     4     373.8 81474 3121.5
## - lunch_type:practice_sport               2    1498.1 83346 3122.9
## - parent_marital_status:is_first_child    3    1869.2 83717 3123.5
## + parent_educ:test_prep                   5     367.9 81480 3123.5
## - parent_educ:parent_marital_status      15    5370.9 87219 3123.7
## + parent_educ:lunch_type                  5     307.2 81541 3124.0
## + parent_marital_status:practice_sport    6     474.3 81374 3124.8
## + ethnic_group:practice_sport             8    1015.8 80832 3124.8
## + ethnic_group:wkly_study_hours           8     786.1 81062 3126.5
## + parent_educ:wkly_study_hours           10    1222.9 80625 3127.3
## + ethnic_group:parent_educ               20    2486.4 79362 3138.0
## 
## Step:  AIC=3113.85
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - practice_sport:transport_means          2     207.3 82847 3111.3
## - parent_educ:practice_sport             10    2516.6 85156 3111.6
## - test_prep:transport_means               1      10.1 82650 3111.9
## - gender:transport_means                  1      13.8 82653 3111.9
## - gender:is_first_child                   1      41.3 82681 3112.2
## - transport_means:wkly_study_hours        2     339.2 82979 3112.3
## - test_prep:parent_marital_status         3     629.1 83269 3112.3
## - lunch_type:is_first_child               1      80.4 82720 3112.4
## - gender:test_prep                        1     135.3 82775 3112.8
## - test_prep:is_first_child                1     142.8 82782 3112.9
## - lunch_type:test_prep                    1     144.5 82784 3112.9
## - lunch_type:wkly_study_hours             2     428.9 83069 3112.9
## - gender:lunch_type                       1     191.2 82831 3113.2
## - gender:practice_sport                   2     488.0 83128 3113.3
## - is_first_child:wkly_study_hours         2     498.0 83138 3113.4
## <none>                                                82640 3113.8
## - ethnic_group:is_first_child             4    1132.4 83772 3113.9
## - ethnic_group:transport_means            4    1167.1 83807 3114.1
## - parent_educ:is_first_child              5    1534.0 84174 3114.7
## - lunch_type:transport_means              1     438.1 83078 3115.0
## - parent_marital_status:transport_means   3    1154.2 83794 3116.0
## + ethnic_group:lunch_type                 4     791.6 81848 3116.2
## + practice_sport:is_first_child           2     203.4 82436 3116.4
## + test_prep:practice_sport                2     188.0 82452 3116.5
## + gender:wkly_study_hours                 2     178.0 82462 3116.6
## - parent_marital_status:wkly_study_hours  6    2096.2 84736 3116.6
## + parent_educ:transport_means             5     990.3 81649 3116.7
## + gender:parent_marital_status            3     400.6 82239 3117.0
## + practice_sport:wkly_study_hours         4     624.4 82015 3117.4
## + ethnic_group:parent_marital_status     10    2132.2 80507 3118.4
## + lunch_type:parent_marital_status        3     186.2 82454 3118.5
## - test_prep:wkly_study_hours              2    1230.2 83870 3118.6
## - is_first_child:transport_means          1     991.0 83631 3118.9
## + ethnic_group:test_prep                  4     387.6 82252 3119.1
## + gender:ethnic_group                     4     380.7 82259 3119.1
## + gender:parent_educ                      5     625.8 82014 3119.4
## - parent_educ:parent_marital_status      15    5161.0 87801 3119.6
## - parent_marital_status:is_first_child    3    1814.6 84454 3120.7
## + parent_educ:test_prep                   5     407.8 82232 3120.9
## - lunch_type:practice_sport               2    1597.2 84237 3121.2
## + parent_educ:lunch_type                  5     333.4 82306 3121.5
## + ethnic_group:practice_sport             8    1057.8 81582 3122.2
## + parent_marital_status:practice_sport    6     482.2 82158 3122.4
## + ethnic_group:wkly_study_hours           8     816.7 81823 3124.0
## + parent_educ:wkly_study_hours           10    1061.0 81579 3126.2
## + ethnic_group:parent_educ               20    2629.1 80011 3134.8
## 
## Step:  AIC=3111.33
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:practice_sport             10    2466.4 85313 3108.6
## - test_prep:transport_means               1       7.1 82854 3109.4
## - gender:transport_means                  1      13.8 82861 3109.4
## - gender:is_first_child                   1      56.2 82903 3109.7
## - lunch_type:is_first_child               1      71.3 82918 3109.8
## - transport_means:wkly_study_hours        2     357.8 83205 3109.9
## - test_prep:parent_marital_status         3     644.8 83492 3109.9
## - gender:test_prep                        1     131.9 82979 3110.3
## - lunch_type:wkly_study_hours             2     420.4 83267 3110.3
## - test_prep:is_first_child                1     147.4 82994 3110.4
## - lunch_type:test_prep                    1     170.0 83017 3110.5
## - gender:practice_sport                   2     458.5 83305 3110.6
## - gender:lunch_type                       1     191.5 83039 3110.7
## - is_first_child:wkly_study_hours         2     491.5 83338 3110.8
## - ethnic_group:is_first_child             4    1114.2 83961 3111.2
## <none>                                                82847 3111.3
## - ethnic_group:transport_means            4    1218.0 84065 3111.9
## - parent_educ:is_first_child              5    1544.3 84391 3112.2
## - lunch_type:transport_means              1     450.3 83297 3112.5
## - parent_marital_status:transport_means   3    1149.8 83997 3113.5
## + practice_sport:transport_means          2     207.3 82640 3113.8
## + ethnic_group:lunch_type                 4     753.5 82094 3113.9
## + gender:wkly_study_hours                 2     193.1 82654 3113.9
## + practice_sport:is_first_child           2     183.8 82663 3114.0
## + test_prep:practice_sport                2     173.2 82674 3114.1
## - parent_marital_status:wkly_study_hours  6    2116.7 84964 3114.2
## + gender:parent_marital_status            3     364.2 82483 3114.7
## + practice_sport:wkly_study_hours         4     605.0 82242 3115.0
## + parent_educ:transport_means             5     874.3 81973 3115.1
## + lunch_type:parent_marital_status        3     180.4 82667 3116.0
## - test_prep:wkly_study_hours              2    1235.2 84082 3116.1
## + ethnic_group:test_prep                  4     396.0 82451 3116.5
## + gender:ethnic_group                     4     377.0 82470 3116.6
## - parent_educ:parent_marital_status      15    5138.6 87986 3116.8
## - is_first_child:transport_means          1    1062.2 83909 3116.8
## + gender:parent_educ                      5     597.8 82249 3117.1
## + ethnic_group:parent_marital_status     10    1954.3 80893 3117.2
## - parent_marital_status:is_first_child    3    1809.3 84656 3118.1
## + parent_educ:test_prep                   5     434.0 82413 3118.2
## - lunch_type:practice_sport               2    1585.6 84433 3118.5
## + parent_educ:lunch_type                  5     376.4 82471 3118.6
## + ethnic_group:practice_sport             8    1073.6 81773 3119.6
## + parent_marital_status:practice_sport    6     447.4 82400 3120.1
## + ethnic_group:wkly_study_hours           8     821.6 82025 3121.4
## + parent_educ:wkly_study_hours           10    1023.1 81824 3124.0
## + ethnic_group:parent_educ               20    2651.9 80195 3132.1
## 
## Step:  AIC=3108.64
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:parent_marital_status + test_prep:is_first_child + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:parent_marital_status         3     528.2 85842 3106.3
## - transport_means:wkly_study_hours        2     252.8 85566 3106.4
## - test_prep:transport_means               1       6.1 85320 3106.7
## - gender:transport_means                  1      53.5 85367 3107.0
## - gender:is_first_child                   1      69.0 85382 3107.1
## - gender:practice_sport                   2     371.9 85685 3107.2
## - lunch_type:is_first_child               1      89.0 85402 3107.2
## - gender:lunch_type                       1     128.6 85442 3107.5
## - lunch_type:test_prep                    1     168.7 85482 3107.8
## - gender:test_prep                        1     169.6 85483 3107.8
## - test_prep:is_first_child                1     189.4 85503 3107.9
## - is_first_child:wkly_study_hours         2     501.2 85815 3108.1
## - lunch_type:wkly_study_hours             2     501.8 85815 3108.1
## <none>                                                85313 3108.6
## - ethnic_group:is_first_child             4    1176.4 86490 3108.7
## - lunch_type:transport_means              1     350.4 85664 3109.1
## - ethnic_group:transport_means            4    1384.3 86698 3110.1
## - test_prep:wkly_study_hours              2     930.9 86244 3111.0
## + parent_educ:practice_sport             10    2466.4 82847 3111.3
## + gender:wkly_study_hours                 2     187.2 85126 3111.3
## - parent_educ:is_first_child              5    1861.6 87175 3111.4
## + practice_sport:is_first_child           2     173.2 85140 3111.4
## + test_prep:practice_sport                2     172.7 85141 3111.4
## + practice_sport:transport_means          2     157.1 85156 3111.6
## + ethnic_group:lunch_type                 4     725.6 84588 3111.6
## - parent_marital_status:wkly_study_hours  6    2229.8 87543 3111.9
## - parent_marital_status:transport_means   3    1345.0 86658 3111.9
## + gender:parent_marital_status            3     380.5 84933 3112.0
## - is_first_child:transport_means          1     813.3 86127 3112.2
## + practice_sport:wkly_study_hours         4     575.3 84738 3112.7
## + parent_educ:transport_means             5     848.1 84465 3112.7
## - lunch_type:practice_sport               2    1258.9 86572 3113.3
## + lunch_type:parent_marital_status        3     167.1 85146 3113.5
## + ethnic_group:test_prep                  4     430.7 84883 3113.7
## + gender:ethnic_group                     4     394.4 84919 3113.9
## + gender:parent_educ                      5     656.9 84657 3114.1
## - parent_marital_status:is_first_child    3    1770.1 87084 3114.8
## + parent_educ:lunch_type                  5     556.2 84757 3114.8
## + parent_educ:test_prep                   5     401.2 84912 3115.9
## + ethnic_group:practice_sport             8    1164.5 84149 3116.5
## - parent_educ:parent_marital_status      15    5674.3 90988 3116.6
## + ethnic_group:parent_marital_status     10    1651.0 83662 3117.1
## + parent_marital_status:practice_sport    6     334.6 84979 3118.3
## + ethnic_group:wkly_study_hours           8     773.4 84540 3119.3
## + parent_educ:wkly_study_hours           10    1137.2 84176 3120.7
## + ethnic_group:parent_educ               20    2585.1 82728 3130.5
## 
## Step:  AIC=3106.28
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - transport_means:wkly_study_hours        2     246.8 86088 3104.0
## - test_prep:transport_means               1      16.2 85858 3104.4
## - gender:transport_means                  1      41.8 85883 3104.6
## - lunch_type:is_first_child               1      80.3 85922 3104.8
## - gender:is_first_child                   1      80.8 85922 3104.8
## - gender:practice_sport                   2     391.2 86233 3105.0
## - gender:lunch_type                       1     133.0 85975 3105.2
## - gender:test_prep                        1     156.6 85998 3105.4
## - lunch_type:test_prep                    1     167.4 86009 3105.4
## - lunch_type:wkly_study_hours             2     517.9 86359 3105.8
## - is_first_child:wkly_study_hours         2     539.2 86381 3106.0
## - test_prep:is_first_child                1     264.1 86106 3106.1
## <none>                                                85842 3106.3
## - ethnic_group:is_first_child             4    1209.8 87051 3106.5
## - lunch_type:transport_means              1     355.0 86197 3106.7
## - ethnic_group:transport_means            4    1370.0 87212 3107.6
## - parent_educ:is_first_child              5    1803.5 87645 3108.6
## - test_prep:wkly_study_hours              2     922.7 86764 3108.6
## + test_prep:parent_marital_status         3     528.2 85313 3108.6
## + test_prep:practice_sport                2     227.2 85614 3108.7
## + ethnic_group:lunch_type                 4     794.7 85047 3108.8
## + gender:wkly_study_hours                 2     191.1 85650 3109.0
## + practice_sport:transport_means          2     166.2 85675 3109.1
## + practice_sport:is_first_child           2     165.9 85676 3109.1
## - parent_marital_status:wkly_study_hours  6    2221.9 88063 3109.4
## - is_first_child:transport_means          1     764.1 86606 3109.5
## + parent_educ:practice_sport             10    2349.8 83492 3109.9
## - parent_marital_status:transport_means   3    1470.4 87312 3110.3
## + gender:parent_marital_status            3     286.9 85555 3110.3
## + parent_educ:transport_means             5     862.9 84979 3110.3
## + practice_sport:wkly_study_hours         4     547.4 85294 3110.5
## - lunch_type:practice_sport               2    1236.0 87078 3110.7
## + lunch_type:parent_marital_status        3     214.5 85627 3110.8
## + gender:ethnic_group                     4     426.1 85415 3111.3
## + ethnic_group:test_prep                  4     419.6 85422 3111.4
## + gender:parent_educ                      5     621.8 85220 3112.0
## + parent_educ:lunch_type                  5     563.6 85278 3112.4
## - parent_educ:parent_marital_status      15    5469.5 91311 3112.7
## - parent_marital_status:is_first_child    3    1845.3 87687 3112.8
## + parent_educ:test_prep                   5     377.3 85464 3113.7
## + ethnic_group:practice_sport             8    1128.8 84713 3114.5
## + parent_marital_status:practice_sport    6     382.9 85459 3115.6
## + ethnic_group:parent_marital_status     11    1760.9 84081 3116.1
## + ethnic_group:wkly_study_hours           8     867.5 84974 3116.3
## + parent_educ:wkly_study_hours           10    1216.0 84626 3117.9
## + ethnic_group:parent_educ               20    2671.7 83170 3127.6
## 
## Step:  AIC=3103.97
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:transport_means               1       7.5 86096 3102.0
## - gender:transport_means                  1      39.1 86127 3102.2
## - gender:is_first_child                   1      67.5 86156 3102.4
## - lunch_type:is_first_child               1      74.0 86162 3102.5
## - gender:lunch_type                       1     121.2 86210 3102.8
## - gender:practice_sport                   2     425.9 86514 3102.9
## - gender:test_prep                        1     140.2 86228 3102.9
## - lunch_type:test_prep                    1     153.5 86242 3103.0
## - lunch_type:wkly_study_hours             2     549.2 86638 3103.7
## - test_prep:is_first_child                1     279.5 86368 3103.9
## <none>                                                86088 3104.0
## - is_first_child:wkly_study_hours         2     592.9 86681 3104.0
## - lunch_type:transport_means              1     345.6 86434 3104.3
## - ethnic_group:is_first_child             4    1229.5 87318 3104.3
## - test_prep:wkly_study_hours              2     872.0 86960 3105.9
## - ethnic_group:transport_means            4    1465.2 87554 3105.9
## + test_prep:practice_sport                2     258.1 85830 3106.2
## + ethnic_group:lunch_type                 4     835.7 85253 3106.2
## + transport_means:wkly_study_hours        2     246.8 85842 3106.3
## + test_prep:parent_marital_status         3     522.1 85566 3106.4
## - parent_educ:is_first_child              5    1848.6 87937 3106.5
## + practice_sport:transport_means          2     184.0 85904 3106.7
## + practice_sport:is_first_child           2     182.1 85906 3106.7
## + gender:wkly_study_hours                 2     180.1 85908 3106.7
## - is_first_child:transport_means          1     769.9 86858 3107.2
## - parent_marital_status:wkly_study_hours  6    2303.2 88392 3107.6
## - parent_marital_status:transport_means   3    1454.0 87542 3107.9
## + practice_sport:wkly_study_hours         4     564.7 85524 3108.1
## + gender:parent_marital_status            3     272.1 85816 3108.1
## + parent_educ:practice_sport             10    2249.6 83839 3108.3
## + parent_educ:transport_means             5     808.8 85280 3108.4
## + lunch_type:parent_marital_status        3     219.1 85869 3108.5
## - lunch_type:practice_sport               2    1254.1 87342 3108.5
## + gender:ethnic_group                     4     458.6 85630 3108.8
## + ethnic_group:test_prep                  4     414.0 85674 3109.1
## + gender:parent_educ                      5     674.2 85414 3109.3
## + parent_educ:lunch_type                  5     590.9 85497 3109.9
## - parent_marital_status:is_first_child    3    1791.3 87880 3110.1
## - parent_educ:parent_marital_status      15    5445.9 91534 3110.2
## + parent_educ:test_prep                   5     377.4 85711 3111.4
## + ethnic_group:practice_sport             8    1152.6 84936 3112.0
## + parent_marital_status:practice_sport    6     396.9 85691 3113.2
## + ethnic_group:parent_marital_status     11    1695.5 84393 3114.2
## + ethnic_group:wkly_study_hours           8     714.6 85374 3115.1
## + parent_educ:wkly_study_hours           10    1220.0 84868 3115.6
## + ethnic_group:parent_educ               20    2613.0 83475 3125.8
## 
## Step:  AIC=3102.03
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:transport_means                  1      42.1 86138 3100.3
## - gender:is_first_child                   1      67.9 86164 3100.5
## - lunch_type:is_first_child               1      77.5 86173 3100.6
## - gender:lunch_type                       1     124.5 86220 3100.9
## - gender:practice_sport                   2     423.6 86519 3100.9
## - gender:test_prep                        1     138.2 86234 3101.0
## - lunch_type:test_prep                    1     154.4 86250 3101.1
## - lunch_type:wkly_study_hours             2     541.9 86638 3101.7
## - test_prep:is_first_child                1     280.9 86377 3101.9
## <none>                                                86096 3102.0
## - is_first_child:wkly_study_hours         2     601.9 86698 3102.1
## - ethnic_group:is_first_child             4    1222.9 87319 3102.3
## - lunch_type:transport_means              1     341.8 86438 3102.4
## - test_prep:wkly_study_hours              2     866.7 86963 3103.9
## + test_prep:transport_means               1       7.5 86088 3104.0
## - ethnic_group:transport_means            4    1483.7 87580 3104.1
## + test_prep:practice_sport                2     258.8 85837 3104.2
## + ethnic_group:lunch_type                 4     837.4 85258 3104.3
## + transport_means:wkly_study_hours        2     238.0 85858 3104.4
## + test_prep:parent_marital_status         3     528.2 85568 3104.4
## - parent_educ:is_first_child              5    1853.3 87949 3104.6
## + practice_sport:is_first_child           2     182.2 85914 3104.8
## + gender:wkly_study_hours                 2     181.4 85914 3104.8
## + practice_sport:transport_means          2     180.8 85915 3104.8
## - is_first_child:transport_means          1     780.2 86876 3105.3
## - parent_marital_status:wkly_study_hours  6    2299.8 88396 3105.6
## - parent_marital_status:transport_means   3    1462.4 87558 3106.0
## + practice_sport:wkly_study_hours         4     564.1 85532 3106.2
## + gender:parent_marital_status            3     270.0 85826 3106.2
## + parent_educ:practice_sport             10    2248.9 83847 3106.4
## + parent_educ:transport_means             5     812.6 85283 3106.4
## + lunch_type:parent_marital_status        3     221.2 85875 3106.5
## - lunch_type:practice_sport               2    1259.1 87355 3106.6
## + gender:ethnic_group                     4     457.3 85638 3106.9
## + ethnic_group:test_prep                  4     413.8 85682 3107.2
## + gender:parent_educ                      5     671.4 85424 3107.4
## + parent_educ:lunch_type                  5     584.8 85511 3108.0
## - parent_marital_status:is_first_child    3    1800.2 87896 3108.2
## - parent_educ:parent_marital_status      15    5477.3 91573 3108.4
## + parent_educ:test_prep                   5     381.9 85714 3109.4
## + ethnic_group:practice_sport             8    1155.8 84940 3110.1
## + parent_marital_status:practice_sport    6     398.4 85697 3111.3
## + ethnic_group:parent_marital_status     11    1694.7 84401 3112.3
## + ethnic_group:wkly_study_hours           8     716.5 85379 3113.1
## + parent_educ:wkly_study_hours           10    1221.4 84874 3113.6
## + ethnic_group:parent_educ               20    2587.1 83509 3124.0
## 
## Step:  AIC=3100.31
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:is_first_child                   1      67.1 86205 3098.8
## - lunch_type:is_first_child               1      87.1 86225 3098.9
## - gender:test_prep                        1     125.8 86264 3099.2
## - gender:lunch_type                       1     127.9 86266 3099.2
## - gender:practice_sport                   2     441.0 86579 3099.3
## - lunch_type:test_prep                    1     157.7 86296 3099.4
## - lunch_type:wkly_study_hours             2     527.4 86665 3099.9
## - test_prep:is_first_child                1     287.0 86425 3100.3
## <none>                                                86138 3100.3
## - is_first_child:wkly_study_hours         2     614.1 86752 3100.5
## - ethnic_group:is_first_child             4    1217.0 87355 3100.6
## - lunch_type:transport_means              1     350.7 86489 3100.7
## + gender:transport_means                  1      42.1 86096 3102.0
## - test_prep:wkly_study_hours              2     865.7 87004 3102.2
## + test_prep:transport_means               1      10.5 86127 3102.2
## - ethnic_group:transport_means            4    1467.2 87605 3102.3
## + test_prep:practice_sport                2     254.5 85883 3102.6
## + ethnic_group:lunch_type                 4     830.4 85308 3102.6
## + transport_means:wkly_study_hours        2     233.9 85904 3102.7
## + test_prep:parent_marital_status         3     517.8 85620 3102.8
## - parent_educ:is_first_child              5    1840.1 87978 3102.8
## + gender:wkly_study_hours                 2     185.9 85952 3103.0
## + practice_sport:is_first_child           2     184.7 85953 3103.1
## + practice_sport:transport_means          2     182.4 85956 3103.1
## - is_first_child:transport_means          1     803.3 86941 3103.8
## - parent_marital_status:wkly_study_hours  6    2297.0 88435 3103.8
## - parent_marital_status:transport_means   3    1462.1 87600 3104.2
## + parent_educ:practice_sport             10    2282.9 83855 3104.5
## + gender:parent_marital_status            3     264.9 85873 3104.5
## + practice_sport:wkly_study_hours         4     542.5 85595 3104.6
## + parent_educ:transport_means             5     823.1 85315 3104.7
## - lunch_type:practice_sport               2    1240.0 87378 3104.8
## + lunch_type:parent_marital_status        3     222.7 85915 3104.8
## + gender:ethnic_group                     4     473.5 85664 3105.1
## + ethnic_group:test_prep                  4     412.7 85725 3105.5
## + gender:parent_educ                      5     671.3 85467 3105.7
## + parent_educ:lunch_type                  5     591.3 85547 3106.2
## - parent_educ:parent_marital_status      15    5443.9 91582 3106.5
## - parent_marital_status:is_first_child    3    1820.2 87958 3106.7
## + parent_educ:test_prep                   5     385.7 85752 3107.7
## + ethnic_group:practice_sport             8    1140.5 84997 3108.4
## + parent_marital_status:practice_sport    6     390.6 85747 3109.6
## + ethnic_group:parent_marital_status     11    1717.1 84421 3110.4
## + ethnic_group:wkly_study_hours           8     709.6 85428 3111.4
## + parent_educ:wkly_study_hours           10    1196.9 84941 3112.1
## + ethnic_group:parent_educ               20    2560.8 83577 3122.5
## 
## Step:  AIC=3098.77
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:is_first_child + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:is_first_child               1      97.8 86303 3097.4
## - gender:test_prep                        1     115.8 86321 3097.6
## - gender:lunch_type                       1     127.1 86332 3097.6
## - gender:practice_sport                   2     456.8 86662 3097.9
## - lunch_type:test_prep                    1     169.6 86375 3097.9
## - lunch_type:wkly_study_hours             2     528.1 86733 3098.4
## <none>                                                86205 3098.8
## - ethnic_group:is_first_child             4    1184.1 87389 3098.8
## - test_prep:is_first_child                1     315.6 86521 3098.9
## - is_first_child:wkly_study_hours         2     648.1 86853 3099.2
## - lunch_type:transport_means              1     367.7 86573 3099.3
## + gender:is_first_child                   1      67.1 86138 3100.3
## + gender:transport_means                  1      41.3 86164 3100.5
## - test_prep:wkly_study_hours              2     849.9 87055 3100.6
## + test_prep:transport_means               1      10.9 86194 3100.7
## - ethnic_group:transport_means            4    1518.3 87723 3101.1
## + test_prep:practice_sport                2     241.4 85964 3101.1
## + ethnic_group:lunch_type                 4     819.4 85386 3101.1
## + test_prep:parent_marital_status         3     527.3 85678 3101.2
## + transport_means:wkly_study_hours        2     221.2 85984 3101.3
## + practice_sport:transport_means          2     193.8 86011 3101.4
## + practice_sport:is_first_child           2     192.0 86013 3101.5
## + gender:wkly_study_hours                 2     185.4 86020 3101.5
## - parent_educ:is_first_child              5    1889.5 88095 3101.6
## - parent_marital_status:wkly_study_hours  6    2259.4 88464 3102.0
## - is_first_child:transport_means          1     777.0 86982 3102.1
## + gender:parent_marital_status            3     287.2 85918 3102.8
## + parent_educ:practice_sport             10    2295.0 83910 3102.8
## + practice_sport:wkly_study_hours         4     562.1 85643 3102.9
## - parent_marital_status:transport_means   3    1506.1 87711 3103.0
## + parent_educ:transport_means             5     813.9 85391 3103.2
## + lunch_type:parent_marital_status        3     232.4 85973 3103.2
## + gender:ethnic_group                     4     489.0 85716 3103.4
## - lunch_type:practice_sport               2    1289.5 87495 3103.5
## + ethnic_group:test_prep                  4     394.8 85810 3104.1
## + gender:parent_educ                      5     664.8 85540 3104.2
## + parent_educ:lunch_type                  5     631.3 85574 3104.4
## - parent_educ:parent_marital_status      15    5457.7 91663 3105.0
## - parent_marital_status:is_first_child    3    1805.4 88011 3105.0
## + parent_educ:test_prep                   5     387.6 85818 3106.1
## + ethnic_group:practice_sport             8    1096.1 85109 3107.2
## + parent_marital_status:practice_sport    6     389.2 85816 3108.1
## + ethnic_group:parent_marital_status     11    1738.0 84467 3108.8
## + ethnic_group:wkly_study_hours           8     685.9 85519 3110.1
## + parent_educ:wkly_study_hours           10    1203.7 85001 3110.5
## + ethnic_group:parent_educ               20    2490.6 83714 3121.5
## 
## Step:  AIC=3097.44
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:lunch_type                       1     120.4 86423 3096.3
## - gender:test_prep                        1     122.5 86425 3096.3
## - gender:practice_sport                   2     425.3 86728 3096.3
## - lunch_type:test_prep                    1     164.4 86467 3096.6
## - lunch_type:wkly_study_hours             2     507.0 86810 3096.9
## - ethnic_group:is_first_child             4    1131.4 87434 3097.1
## <none>                                                86303 3097.4
## - test_prep:is_first_child                1     293.8 86597 3097.4
## - is_first_child:wkly_study_hours         2     610.4 86913 3097.6
## - lunch_type:transport_means              1     380.8 86684 3098.0
## + lunch_type:is_first_child               1      97.8 86205 3098.8
## + gender:is_first_child                   1      77.8 86225 3098.9
## + gender:transport_means                  1      51.4 86251 3099.1
## - test_prep:wkly_study_hours              2     862.1 87165 3099.3
## + test_prep:transport_means               1      16.2 86287 3099.3
## + ethnic_group:lunch_type                 4     823.2 85480 3099.8
## + test_prep:practice_sport                2     235.1 86068 3099.8
## + test_prep:parent_marital_status         3     520.4 85782 3099.9
## - ethnic_group:transport_means            4    1548.9 87852 3099.9
## + transport_means:wkly_study_hours        2     211.8 86091 3100.0
## + gender:wkly_study_hours                 2     188.5 86114 3100.2
## + practice_sport:transport_means          2     184.2 86119 3100.2
## - parent_educ:is_first_child              5    1885.0 88188 3100.2
## + practice_sport:is_first_child           2     175.0 86128 3100.2
## - parent_marital_status:wkly_study_hours  6    2200.8 88504 3100.3
## - is_first_child:transport_means          1     770.4 87073 3100.7
## + practice_sport:wkly_study_hours         4     603.6 85699 3101.3
## + parent_educ:practice_sport             10    2322.3 83981 3101.3
## + gender:parent_marital_status            3     297.0 86006 3101.4
## - parent_marital_status:transport_means   3    1515.9 87819 3101.7
## + parent_educ:transport_means             5     822.3 85481 3101.8
## + lunch_type:parent_marital_status        3     227.7 86075 3101.9
## - lunch_type:practice_sport               2    1285.2 87588 3102.2
## + gender:ethnic_group                     4     468.8 85834 3102.2
## + ethnic_group:test_prep                  4     412.9 85890 3102.6
## + gender:parent_educ                      5     671.5 85631 3102.8
## + parent_educ:lunch_type                  5     648.6 85654 3103.0
## - parent_marital_status:is_first_child    3    1733.5 88036 3103.2
## - parent_educ:parent_marital_status      15    5422.1 91725 3103.4
## + parent_educ:test_prep                   5     411.8 85891 3104.6
## + ethnic_group:practice_sport             8    1075.2 85228 3106.1
## + parent_marital_status:practice_sport    6     390.2 85913 3106.8
## + ethnic_group:parent_marital_status     11    1745.0 84558 3107.4
## + ethnic_group:wkly_study_hours           8     686.4 85616 3108.7
## + parent_educ:wkly_study_hours           10    1226.0 85077 3109.0
## + ethnic_group:parent_educ               20    2445.0 83858 3120.5
## 
## Step:  AIC=3096.27
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:test_prep + gender:practice_sport + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:is_first_child + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:test_prep                        1     108.1 86531 3095.0
## - gender:practice_sport                   2     419.0 86842 3095.1
## - lunch_type:test_prep                    1     190.0 86613 3095.6
## - lunch_type:wkly_study_hours             2     492.0 86915 3095.6
## - ethnic_group:is_first_child             4    1110.9 87534 3095.8
## <none>                                                86423 3096.3
## - test_prep:is_first_child                1     303.9 86727 3096.3
## - is_first_child:wkly_study_hours         2     606.7 87030 3096.4
## - lunch_type:transport_means              1     408.7 86832 3097.1
## + gender:lunch_type                       1     120.4 86303 3097.4
## + lunch_type:is_first_child               1      91.2 86332 3097.6
## + gender:is_first_child                   1      76.5 86347 3097.7
## + gender:transport_means                  1      54.6 86369 3097.9
## + test_prep:transport_means               1      20.8 86403 3098.1
## - test_prep:wkly_study_hours              2     879.1 87302 3098.2
## + test_prep:practice_sport                2     250.2 86173 3098.6
## + ethnic_group:lunch_type                 4     828.1 85595 3098.6
## + test_prep:parent_marital_status         3     526.2 85897 3098.7
## + transport_means:wkly_study_hours        2     200.0 86223 3098.9
## - ethnic_group:transport_means            4    1576.0 87999 3098.9
## + practice_sport:transport_means          2     181.2 86242 3099.0
## + gender:wkly_study_hours                 2     166.1 86257 3099.1
## + practice_sport:is_first_child           2     161.1 86262 3099.2
## - parent_educ:is_first_child              5    1917.3 88341 3099.2
## - is_first_child:transport_means          1     743.5 87167 3099.3
## - parent_marital_status:wkly_study_hours  6    2284.1 88707 3099.7
## + practice_sport:wkly_study_hours         4     602.7 85821 3100.1
## - parent_marital_status:transport_means   3    1475.8 87899 3100.3
## + gender:parent_marital_status            3     286.4 86137 3100.3
## + parent_educ:transport_means             5     855.6 85568 3100.4
## + parent_educ:practice_sport             10    2280.1 84143 3100.5
## + lunch_type:parent_marital_status        3     258.2 86165 3100.5
## + gender:ethnic_group                     4     457.4 85966 3101.1
## + ethnic_group:test_prep                  4     418.7 86005 3101.4
## + parent_educ:lunch_type                  5     696.7 85727 3101.5
## - lunch_type:practice_sport               2    1371.9 87795 3101.6
## - parent_marital_status:is_first_child    3    1685.0 88108 3101.7
## + gender:parent_educ                      5     664.3 85759 3101.7
## - parent_educ:parent_marital_status      15    5394.8 91818 3102.0
## + parent_educ:test_prep                   5     394.9 86028 3103.6
## + ethnic_group:practice_sport             8    1026.1 85397 3105.2
## + parent_marital_status:practice_sport    6     401.4 86022 3105.5
## + ethnic_group:parent_marital_status     11    1748.2 84675 3106.2
## + ethnic_group:wkly_study_hours           8     702.1 85721 3107.4
## + parent_educ:wkly_study_hours           10    1177.1 85246 3108.2
## + ethnic_group:parent_educ               20    2371.1 84052 3119.8
## 
## Step:  AIC=3095
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:is_first_child + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:practice_sport                   2     441.2 86973 3094.0
## - ethnic_group:is_first_child             4    1074.7 87606 3094.3
## - lunch_type:test_prep                    1     207.3 86739 3094.4
## - lunch_type:wkly_study_hours             2     504.2 87036 3094.4
## <none>                                                86531 3095.0
## - test_prep:is_first_child                1     303.6 86835 3095.1
## - is_first_child:wkly_study_hours         2     612.5 87144 3095.2
## - lunch_type:transport_means              1     426.8 86958 3095.9
## + gender:test_prep                        1     108.1 86423 3096.3
## + gender:lunch_type                       1     106.0 86425 3096.3
## + lunch_type:is_first_child               1      97.7 86434 3096.3
## + gender:is_first_child                   1      66.6 86465 3096.6
## + gender:transport_means                  1      41.4 86490 3096.7
## - test_prep:wkly_study_hours              2     845.9 87377 3096.7
## + test_prep:transport_means               1      17.0 86514 3096.9
## + ethnic_group:lunch_type                 4     846.4 85685 3097.2
## + test_prep:practice_sport                2     243.1 86288 3097.3
## + test_prep:parent_marital_status         3     516.8 86015 3097.5
## - parent_educ:is_first_child              5    1876.5 88408 3097.7
## + gender:wkly_study_hours                 2     188.8 86343 3097.7
## + transport_means:wkly_study_hours        2     188.1 86343 3097.7
## - ethnic_group:transport_means            4    1587.4 88119 3097.7
## + practice_sport:transport_means          2     173.6 86358 3097.8
## + practice_sport:is_first_child           2     167.8 86364 3097.9
## - is_first_child:transport_means          1     725.6 87257 3097.9
## - parent_marital_status:wkly_study_hours  6    2257.5 88789 3098.2
## + practice_sport:wkly_study_hours         4     589.5 85942 3099.0
## + gender:parent_marital_status            3     295.0 86236 3099.0
## + parent_educ:practice_sport             10    2314.6 84217 3099.0
## - parent_marital_status:transport_means   3    1496.6 88028 3099.1
## + lunch_type:parent_marital_status        3     270.6 86261 3099.2
## + parent_educ:transport_means             5     842.4 85689 3099.2
## + gender:ethnic_group                     4     451.2 86080 3099.9
## - parent_marital_status:is_first_child    3    1638.4 88170 3100.1
## - lunch_type:practice_sport               2    1356.7 87888 3100.2
## + parent_educ:lunch_type                  5     696.7 85835 3100.2
## + ethnic_group:test_prep                  4     384.9 86146 3100.4
## - parent_educ:parent_marital_status      15    5349.4 91881 3100.4
## + gender:parent_educ                      5     657.1 85874 3100.5
## + parent_educ:test_prep                   5     396.0 86135 3102.3
## + parent_marital_status:practice_sport    6     425.7 86106 3104.1
## + ethnic_group:practice_sport             8     993.6 85538 3104.2
## + ethnic_group:parent_marital_status     11    1802.0 84729 3104.6
## + ethnic_group:wkly_study_hours           8     733.7 85798 3106.0
## + parent_educ:wkly_study_hours           10    1223.2 85308 3106.6
## + ethnic_group:parent_educ               20    2369.4 84162 3118.6
## 
## Step:  AIC=3094
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:is_first_child             4    1045.7 88018 3093.1
## - lunch_type:wkly_study_hours             2     485.3 87458 3093.3
## - lunch_type:test_prep                    1     212.0 87185 3093.4
## - test_prep:is_first_child                1     279.8 87252 3093.9
## <none>                                                86973 3094.0
## - is_first_child:wkly_study_hours         2     618.8 87591 3094.2
## + gender:practice_sport                   2     441.2 86531 3095.0
## + gender:test_prep                        1     130.3 86842 3095.1
## - lunch_type:transport_means              1     467.1 87440 3095.2
## + gender:lunch_type                       1      98.8 86874 3095.3
## + gender:is_first_child                   1      77.3 86895 3095.5
## + lunch_type:is_first_child               1      67.1 86905 3095.6
## + gender:transport_means                  1      55.4 86917 3095.6
## - test_prep:wkly_study_hours              2     847.3 87820 3095.7
## + test_prep:transport_means               1      12.9 86960 3095.9
## + test_prep:practice_sport                2     266.7 86706 3096.2
## - parent_marital_status:wkly_study_hours  6    2123.6 89096 3096.2
## + test_prep:parent_marital_status         3     531.6 86441 3096.4
## + gender:wkly_study_hours                 2     221.6 86751 3096.5
## + transport_means:wkly_study_hours        2     219.6 86753 3096.5
## - ethnic_group:transport_means            4    1578.3 88551 3096.6
## - parent_educ:is_first_child              5    1897.3 88870 3096.7
## + ethnic_group:lunch_type                 4     771.2 86201 3096.8
## + practice_sport:is_first_child           2     167.3 86805 3096.9
## + practice_sport:transport_means          2     155.6 86817 3096.9
## - is_first_child:transport_means          1     764.2 87737 3097.2
## - parent_marital_status:transport_means   3    1428.3 88401 3097.6
## + gender:parent_marital_status            3     346.2 86626 3097.7
## + practice_sport:wkly_study_hours         4     637.1 86335 3097.7
## + parent_educ:transport_means             5     864.0 86109 3098.1
## + lunch_type:parent_marital_status        3     267.4 86705 3098.2
## + parent_educ:practice_sport             10    2207.6 84765 3098.8
## + parent_educ:lunch_type                  5     741.3 86231 3098.9
## + gender:ethnic_group                     4     414.5 86558 3099.2
## - parent_educ:parent_marital_status      15    5364.1 92337 3099.3
## - parent_marital_status:is_first_child    3    1684.3 88657 3099.3
## + ethnic_group:test_prep                  4     382.9 86590 3099.4
## + gender:parent_educ                      5     657.1 86316 3099.5
## - lunch_type:practice_sport               2    1466.3 88439 3099.9
## + parent_educ:test_prep                   5     353.3 86619 3101.6
## + ethnic_group:practice_sport             8    1131.7 85841 3102.3
## + parent_marital_status:practice_sport    6     408.6 86564 3103.2
## + ethnic_group:parent_marital_status     11    1849.7 85123 3103.3
## + ethnic_group:wkly_study_hours           8     736.7 86236 3105.0
## + parent_educ:wkly_study_hours           10    1160.6 85812 3106.1
## - gender                                  1    2914.0 89887 3111.4
## + ethnic_group:parent_educ               20    2455.9 84517 3117.1
## 
## Step:  AIC=3093.05
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:is_first_child + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:wkly_study_hours             2     439.6 88458 3092.0
## - lunch_type:test_prep                    1     220.6 88239 3092.5
## <none>                                                88018 3093.1
## - test_prep:is_first_child                1     327.4 88346 3093.2
## - test_prep:wkly_study_hours              2     638.7 88657 3093.3
## - lunch_type:transport_means              1     406.7 88425 3093.8
## + ethnic_group:is_first_child             4    1045.7 86973 3094.0
## - is_first_child:wkly_study_hours         2     753.2 88772 3094.1
## + gender:practice_sport                   2     412.2 87606 3094.3
## - is_first_child:transport_means          1     504.9 88523 3094.4
## + gender:test_prep                        1      91.6 87927 3094.4
## + gender:lunch_type                       1      84.2 87934 3094.5
## + gender:transport_means                  1      45.0 87973 3094.8
## + gender:is_first_child                   1      42.5 87976 3094.8
## - parent_marital_status:wkly_study_hours  6    2077.1 90095 3094.8
## + lunch_type:is_first_child               1      25.4 87993 3094.9
## + test_prep:transport_means               1       2.9 88015 3095.0
## + test_prep:practice_sport                2     279.7 87739 3095.2
## + test_prep:parent_marital_status         3     571.5 87447 3095.2
## + transport_means:wkly_study_hours        2     250.1 87768 3095.4
## + practice_sport:is_first_child           2     227.8 87790 3095.5
## - ethnic_group:transport_means            4    1651.1 89669 3096.0
## + gender:wkly_study_hours                 2     139.5 87879 3096.1
## + practice_sport:transport_means          2     136.1 87882 3096.1
## + practice_sport:wkly_study_hours         4     699.2 87319 3096.3
## - parent_educ:is_first_child              5    2019.8 90038 3096.4
## - parent_marital_status:transport_means   3    1460.3 89479 3096.8
## + parent_educ:transport_means             5     915.0 87103 3096.9
## + gender:parent_marital_status            3     278.5 87740 3097.2
## + ethnic_group:lunch_type                 4     559.4 87459 3097.3
## - parent_educ:parent_marital_status      15    5295.5 93314 3097.5
## + lunch_type:parent_marital_status        3     226.5 87792 3097.5
## + parent_educ:lunch_type                  5     815.5 87203 3097.6
## + parent_educ:practice_sport             10    2279.3 85739 3097.6
## + ethnic_group:test_prep                  4     411.9 87606 3098.3
## - lunch_type:practice_sport               2    1396.6 89415 3098.3
## + gender:ethnic_group                     4     377.8 87641 3098.5
## - parent_marital_status:is_first_child    3    1836.6 89855 3099.2
## + gender:parent_educ                      5     561.0 87457 3099.3
## + parent_educ:test_prep                   5     377.5 87641 3100.5
## + ethnic_group:practice_sport             8    1053.2 86965 3101.9
## + parent_marital_status:practice_sport    6     283.5 87735 3103.2
## + ethnic_group:wkly_study_hours           8     783.8 87235 3103.8
## + ethnic_group:parent_marital_status     11    1528.1 86490 3104.7
## + parent_educ:wkly_study_hours           10    1203.3 86815 3104.9
## - gender                                  1    3194.3 91213 3112.1
## + ethnic_group:parent_educ               20    2547.3 85471 3115.7
## 
## Step:  AIC=3091.99
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means + 
##     test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:test_prep                    1     183.8 88642 3091.2
## <none>                                                88458 3092.0
## - test_prep:is_first_child                1     353.8 88812 3092.3
## - lunch_type:transport_means              1     389.2 88847 3092.6
## - test_prep:wkly_study_hours              2     693.4 89151 3092.6
## - parent_marital_status:wkly_study_hours  6    1937.5 90395 3092.8
## + lunch_type:wkly_study_hours             2     439.6 88018 3093.1
## - is_first_child:wkly_study_hours         2     763.2 89221 3093.1
## + ethnic_group:is_first_child             4    1000.0 87458 3093.3
## + gender:test_prep                        1     103.6 88354 3093.3
## + gender:practice_sport                   2     395.2 88063 3093.3
## + gender:lunch_type                       1      74.0 88384 3093.5
## - is_first_child:transport_means          1     556.8 89015 3093.7
## + gender:is_first_child                   1      40.5 88417 3093.7
## + gender:transport_means                  1      29.5 88428 3093.8
## + test_prep:practice_sport                2     322.7 88135 3093.8
## + lunch_type:is_first_child               1      16.5 88441 3093.9
## + test_prep:transport_means               1       1.5 88456 3094.0
## + transport_means:wkly_study_hours        2     289.0 88169 3094.1
## + test_prep:parent_marital_status         3     573.8 87884 3094.2
## + practice_sport:is_first_child           2     234.2 88224 3094.4
## - ethnic_group:transport_means            4    1593.9 90052 3094.5
## - parent_educ:is_first_child              5    1983.0 90441 3095.1
## + practice_sport:transport_means          2     128.9 88329 3095.1
## + gender:wkly_study_hours                 2     103.0 88355 3095.3
## + parent_educ:transport_means             5     988.3 87470 3095.4
## - parent_marital_status:transport_means   3    1439.2 89897 3095.5
## + practice_sport:wkly_study_hours         4     664.7 87793 3095.5
## + gender:parent_marital_status            3     332.0 88126 3095.8
## + parent_educ:practice_sport             10    2350.0 86108 3096.1
## + lunch_type:parent_marital_status        3     206.8 88251 3096.6
## + ethnic_group:lunch_type                 4     504.4 87953 3096.6
## - parent_educ:parent_marital_status      15    5358.7 93817 3096.7
## + ethnic_group:test_prep                  4     423.2 88035 3097.2
## + parent_educ:lunch_type                  5     709.1 87749 3097.2
## - lunch_type:practice_sport               2    1411.9 89870 3097.3
## + gender:ethnic_group                     4     346.1 88112 3097.7
## + gender:parent_educ                      5     616.5 87841 3097.9
## - parent_marital_status:is_first_child    3    1837.0 90295 3098.1
## + parent_educ:test_prep                   5     386.1 88072 3099.4
## + ethnic_group:practice_sport             8    1034.5 87423 3101.1
## + parent_marital_status:practice_sport    6     290.1 88168 3102.1
## + ethnic_group:wkly_study_hours           8     803.7 87654 3102.6
## + ethnic_group:parent_marital_status     11    1478.6 86979 3104.1
## + parent_educ:wkly_study_hours           10    1132.5 87325 3104.4
## - gender                                  1    3238.9 91697 3111.2
## + ethnic_group:parent_educ               20    2566.2 85892 3114.6
## 
## Step:  AIC=3091.22
## math_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:practice_sport + lunch_type:transport_means + 
##     test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## <none>                                                88642 3091.2
## - test_prep:is_first_child                1     340.8 88982 3091.5
## - lunch_type:transport_means              1     343.0 88985 3091.5
## - test_prep:wkly_study_hours              2     699.0 89341 3091.8
## + lunch_type:test_prep                    1     183.8 88458 3092.0
## - parent_marital_status:wkly_study_hours  6    1959.2 90601 3092.1
## + gender:test_prep                        1     118.0 88524 3092.4
## + ethnic_group:is_first_child             4    1007.9 87634 3092.5
## + lunch_type:wkly_study_hours             2     402.8 88239 3092.5
## + gender:practice_sport                   2     399.7 88242 3092.6
## - is_first_child:wkly_study_hours         2     806.1 89448 3092.6
## - is_first_child:transport_means          1     504.9 89147 3092.6
## + gender:lunch_type                       1      94.2 88547 3092.6
## + gender:is_first_child                   1      46.8 88595 3092.9
## + gender:transport_means                  1      33.6 88608 3093.0
## + test_prep:practice_sport                2     332.6 88309 3093.0
## + lunch_type:is_first_child               1      14.2 88627 3093.1
## + test_prep:transport_means               1       0.9 88641 3093.2
## + test_prep:parent_marital_status         3     572.8 88069 3093.4
## + transport_means:wkly_study_hours        2     262.7 88379 3093.5
## + practice_sport:is_first_child           2     245.6 88396 3093.6
## - ethnic_group:transport_means            4    1620.7 90262 3093.9
## - parent_educ:is_first_child              5    1937.1 90579 3094.0
## + practice_sport:transport_means          2     152.2 88490 3094.2
## + gender:wkly_study_hours                 2     104.4 88537 3094.5
## + practice_sport:wkly_study_hours         4     694.6 87947 3094.6
## + parent_educ:transport_means             5     980.6 87661 3094.7
## - parent_marital_status:transport_means   3    1457.2 90099 3094.8
## + gender:parent_marital_status            3     336.0 88306 3095.0
## - parent_educ:parent_marital_status      15    5267.7 93909 3095.3
## + parent_educ:practice_sport             10    2356.5 86285 3095.3
## + ethnic_group:lunch_type                 4     527.6 88114 3095.7
## + lunch_type:parent_marital_status        3     190.8 88451 3095.9
## - lunch_type:practice_sport               2    1378.2 90020 3096.3
## + ethnic_group:test_prep                  4     405.7 88236 3096.5
## + parent_educ:lunch_type                  5     676.9 87965 3096.7
## + gender:ethnic_group                     4     349.9 88292 3096.9
## + gender:parent_educ                      5     646.5 87995 3096.9
## - parent_marital_status:is_first_child    3    1860.2 90502 3097.5
## + parent_educ:test_prep                   5     412.2 88229 3098.5
## + ethnic_group:practice_sport             8    1081.3 87560 3100.0
## + parent_marital_status:practice_sport    6     299.4 88342 3101.2
## + ethnic_group:wkly_study_hours           8     857.1 87785 3101.5
## + parent_educ:wkly_study_hours           10    1206.0 87436 3103.1
## + ethnic_group:parent_marital_status     11    1444.1 87198 3103.5
## - gender                                  1    3294.9 91937 3110.8
## + ethnic_group:parent_educ               20    2571.4 86070 3113.8
summary(stepwise_model_math)
## 
## Call:
## lm(formula = math_score ~ gender + ethnic_group + parent_educ + 
##     lunch_type + test_prep + parent_marital_status + practice_sport + 
##     is_first_child + transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:is_first_child + 
##     lunch_type:practice_sport + lunch_type:transport_means + 
##     test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours, 
##     data = df_4_mdl_math)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -48.225  -8.356   0.435   8.408  29.970 
## 
## Coefficients:
##                                                           Estimate Std. Error
## (Intercept)                                                43.4922     7.6094
## gendermale                                                  5.0562     1.1468
## ethnic_groupgroup B                                         3.1099     3.8855
## ethnic_groupgroup C                                         4.7867     3.5363
## ethnic_groupgroup D                                         4.4789     3.6141
## ethnic_groupgroup E                                        19.5605     4.0197
## parent_educbachelor's degree                               22.6142     6.3793
## parent_educhigh school                                    -11.9676     5.2257
## parent_educmaster's degree                                 -1.9384     7.3940
## parent_educsome college                                     0.8824     5.2535
## parent_educsome high school                                 1.6696     5.2602
## lunch_typestandard                                          5.7052     3.8861
## test_prepnone                                              -1.1067     3.0821
## parent_marital_statusmarried                                9.7202     5.4642
## parent_marital_statussingle                                 3.7791     6.1207
## parent_marital_statuswidowed                               29.2538    21.3074
## practice_sportregularly                                    -4.2709     3.3825
## practice_sportsometimes                                    -6.0415     3.2607
## is_first_childyes                                          12.5726     5.4684
## transport_meansschool_bus                                   5.2495     5.3829
## wkly_study_hours> 10                                       -4.8803     6.2686
## wkly_study_hours10-May                                      4.6584     4.6603
## ethnic_groupgroup B:transport_meansschool_bus              -4.3677     4.8098
## ethnic_groupgroup C:transport_meansschool_bus              -7.7457     4.4977
## ethnic_groupgroup D:transport_meansschool_bus              -0.9133     4.5777
## ethnic_groupgroup E:transport_meansschool_bus             -10.3518     5.0390
## parent_educbachelor's degree:parent_marital_statusmarried -18.4745     6.5736
## parent_educhigh school:parent_marital_statusmarried         0.7418     4.8751
## parent_educmaster's degree:parent_marital_statusmarried     1.1993     6.6521
## parent_educsome college:parent_marital_statusmarried       -7.4232     4.9354
## parent_educsome high school:parent_marital_statusmarried   -8.2283     4.9536
## parent_educbachelor's degree:parent_marital_statussingle  -23.6304     7.4269
## parent_educhigh school:parent_marital_statussingle          1.7141     5.5986
## parent_educmaster's degree:parent_marital_statussingle     -0.6344     7.3500
## parent_educsome college:parent_marital_statussingle       -11.5881     5.6728
## parent_educsome high school:parent_marital_statussingle   -11.5407     5.5591
## parent_educbachelor's degree:parent_marital_statuswidowed -33.5004    17.3280
## parent_educhigh school:parent_marital_statuswidowed       -46.5554    20.4448
## parent_educmaster's degree:parent_marital_statuswidowed   -48.9590    29.6690
## parent_educsome college:parent_marital_statuswidowed      -15.7099    19.0668
## parent_educsome high school:parent_marital_statuswidowed  -19.2638    19.6446
## parent_educbachelor's degree:is_first_childyes             -3.3589     4.3330
## parent_educhigh school:is_first_childyes                    8.9969     3.8002
## parent_educmaster's degree:is_first_childyes                4.7183     5.6364
## parent_educsome college:is_first_childyes                   6.6947     3.7542
## parent_educsome high school:is_first_childyes               2.0436     3.7438
## lunch_typestandard:practice_sportregularly                  8.4203     4.1608
## lunch_typestandard:practice_sportsometimes                 11.3662     4.0244
## lunch_typestandard:transport_meansschool_bus               -3.4368     2.4159
## test_prepnone:is_first_childyes                            -3.6884     2.6012
## test_prepnone:wkly_study_hours> 10                         -6.2865     3.6457
## test_prepnone:wkly_study_hours10-May                       -0.1976     2.8984
## parent_marital_statusmarried:is_first_childyes             -8.7047     3.9485
## parent_marital_statussingle:is_first_childyes              -1.9060     4.3893
## parent_marital_statuswidowed:is_first_childyes             13.7975    13.4714
## parent_marital_statusmarried:transport_meansschool_bus      7.2707     3.3639
## parent_marital_statussingle:transport_meansschool_bus       2.4715     3.7983
## parent_marital_statuswidowed:transport_meansschool_bus    -14.6085    12.8542
## parent_marital_statusmarried:wkly_study_hours> 10          11.6354     5.1480
## parent_marital_statussingle:wkly_study_hours> 10           18.6339     5.7474
## parent_marital_statuswidowed:wkly_study_hours> 10          11.9898    16.7894
## parent_marital_statusmarried:wkly_study_hours10-May         2.1127     3.7866
## parent_marital_statussingle:wkly_study_hours10-May          5.6965     4.2936
## parent_marital_statuswidowed:wkly_study_hours10-May        11.8849    14.3211
## is_first_childyes:transport_meansschool_bus                -4.4000     2.5494
## is_first_childyes:wkly_study_hours> 10                     -0.6479     3.7705
## is_first_childyes:wkly_study_hours10-May                   -5.6646     2.8793
##                                                           t value Pr(>|t|)    
## (Intercept)                                                 5.716 1.84e-08 ***
## gendermale                                                  4.409 1.26e-05 ***
## ethnic_groupgroup B                                         0.800 0.423863    
## ethnic_groupgroup C                                         1.354 0.176457    
## ethnic_groupgroup D                                         1.239 0.215799    
## ethnic_groupgroup E                                         4.866 1.51e-06 ***
## parent_educbachelor's degree                                3.545 0.000428 ***
## parent_educhigh school                                     -2.290 0.022411 *  
## parent_educmaster's degree                                 -0.262 0.793302    
## parent_educsome college                                     0.168 0.866672    
## parent_educsome high school                                 0.317 0.751071    
## lunch_typestandard                                          1.468 0.142671    
## test_prepnone                                              -0.359 0.719670    
## parent_marital_statusmarried                                1.779 0.075838 .  
## parent_marital_statussingle                                 0.617 0.537217    
## parent_marital_statuswidowed                                1.373 0.170360    
## practice_sportregularly                                    -1.263 0.207275    
## practice_sportsometimes                                    -1.853 0.064470 .  
## is_first_childyes                                           2.299 0.021890 *  
## transport_meansschool_bus                                   0.975 0.329901    
## wkly_study_hours> 10                                       -0.779 0.436602    
## wkly_study_hours10-May                                      1.000 0.317963    
## ethnic_groupgroup B:transport_meansschool_bus              -0.908 0.364253    
## ethnic_groupgroup C:transport_meansschool_bus              -1.722 0.085632 .  
## ethnic_groupgroup D:transport_meansschool_bus              -0.200 0.841936    
## ethnic_groupgroup E:transport_meansschool_bus              -2.054 0.040440 *  
## parent_educbachelor's degree:parent_marital_statusmarried  -2.810 0.005133 ** 
## parent_educhigh school:parent_marital_statusmarried         0.152 0.879115    
## parent_educmaster's degree:parent_marital_statusmarried     0.180 0.856998    
## parent_educsome college:parent_marital_statusmarried       -1.504 0.133168    
## parent_educsome high school:parent_marital_statusmarried   -1.661 0.097298 .  
## parent_educbachelor's degree:parent_marital_statussingle   -3.182 0.001551 ** 
## parent_educhigh school:parent_marital_statussingle          0.306 0.759606    
## parent_educmaster's degree:parent_marital_statussingle     -0.086 0.931250    
## parent_educsome college:parent_marital_statussingle        -2.043 0.041580 *  
## parent_educsome high school:parent_marital_statussingle    -2.076 0.038380 *  
## parent_educbachelor's degree:parent_marital_statuswidowed  -1.933 0.053737 .  
## parent_educhigh school:parent_marital_statuswidowed        -2.277 0.023182 *  
## parent_educmaster's degree:parent_marital_statuswidowed    -1.650 0.099508 .  
## parent_educsome college:parent_marital_statuswidowed       -0.824 0.410350    
## parent_educsome high school:parent_marital_statuswidowed   -0.981 0.327238    
## parent_educbachelor's degree:is_first_childyes             -0.775 0.438573    
## parent_educhigh school:is_first_childyes                    2.368 0.018271 *  
## parent_educmaster's degree:is_first_childyes                0.837 0.402905    
## parent_educsome college:is_first_childyes                   1.783 0.075121 .  
## parent_educsome high school:is_first_childyes               0.546 0.585404    
## lunch_typestandard:practice_sportregularly                  2.024 0.043509 *  
## lunch_typestandard:practice_sportsometimes                  2.824 0.004918 ** 
## lunch_typestandard:transport_meansschool_bus               -1.423 0.155457    
## test_prepnone:is_first_childyes                            -1.418 0.156801    
## test_prepnone:wkly_study_hours> 10                         -1.724 0.085236 .  
## test_prepnone:wkly_study_hours10-May                       -0.068 0.945661    
## parent_marital_statusmarried:is_first_childyes             -2.205 0.027922 *  
## parent_marital_statussingle:is_first_childyes              -0.434 0.664285    
## parent_marital_statuswidowed:is_first_childyes              1.024 0.306211    
## parent_marital_statusmarried:transport_meansschool_bus      2.161 0.031117 *  
## parent_marital_statussingle:transport_meansschool_bus       0.651 0.515535    
## parent_marital_statuswidowed:transport_meansschool_bus     -1.136 0.256279    
## parent_marital_statusmarried:wkly_study_hours> 10           2.260 0.024220 *  
## parent_marital_statussingle:wkly_study_hours> 10            3.242 0.001262 ** 
## parent_marital_statuswidowed:wkly_study_hours> 10           0.714 0.475465    
## parent_marital_statusmarried:wkly_study_hours10-May         0.558 0.577124    
## parent_marital_statussingle:wkly_study_hours10-May          1.327 0.185170    
## parent_marital_statuswidowed:wkly_study_hours10-May         0.830 0.406980    
## is_first_childyes:transport_meansschool_bus                -1.726 0.084951 .  
## is_first_childyes:wkly_study_hours> 10                     -0.172 0.863627    
## is_first_childyes:wkly_study_hours10-May                   -1.967 0.049669 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 13.02 on 523 degrees of freedom
## Multiple R-squared:  0.4207, Adjusted R-squared:  0.3476 
## F-statistic: 5.755 on 66 and 523 DF,  p-value: < 2.2e-16

REading Score

df_4_mdl_read=test_df %>% dplyr::select(gender,ethnic_group,parent_educ,lunch_type,test_prep,parent_marital_status,practice_sport,is_first_child,transport_means,wkly_study_hours,reading_score)
full_fit_read=lm(reading_score ~ .^2,data=df_4_mdl_read)
summary(full_fit_read)
## 
## Call:
## lm(formula = reading_score ~ .^2, data = df_4_mdl_read)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -34.758  -7.294   0.000   7.418  27.742 
## 
## Coefficients: (4 not defined because of singularities)
##                                                             Estimate Std. Error
## (Intercept)                                                81.321731  17.167189
## gendermale                                                -12.452051   8.746220
## ethnic_groupgroup B                                       -22.239861  14.760619
## ethnic_groupgroup C                                       -29.866442  13.925159
## ethnic_groupgroup D                                       -14.526414  15.158345
## ethnic_groupgroup E                                       -12.302699  14.206212
## parent_educbachelor's degree                               33.009059  15.519735
## parent_educhigh school                                     10.568006  12.847471
## parent_educmaster's degree                                -24.461817  21.208891
## parent_educsome college                                    -8.316968  12.606066
## parent_educsome high school                                -4.455992  12.227987
## lunch_typestandard                                          2.962788   8.683223
## test_prepnone                                             -21.345506   9.059903
## parent_marital_statusmarried                               16.095657  11.535602
## parent_marital_statussingle                                 5.120602  13.883607
## parent_marital_statuswidowed                               30.884374  41.015667
## practice_sportregularly                                   -22.428022  13.810663
## practice_sportsometimes                                   -19.634669  13.740867
## is_first_childyes                                          16.375726   9.948217
## transport_meansschool_bus                                  -1.212990   8.806349
## wkly_study_hours> 10                                      -17.887902  13.565927
## wkly_study_hours10-May                                      6.195369  10.901941
## gendermale:ethnic_groupgroup B                              7.922999   5.540120
## gendermale:ethnic_groupgroup C                             12.191147   5.327795
## gendermale:ethnic_groupgroup D                              8.192752   5.292503
## gendermale:ethnic_groupgroup E                              9.251399   5.868168
## gendermale:parent_educbachelor's degree                    -2.815989   4.660163
## gendermale:parent_educhigh school                           0.610374   3.800446
## gendermale:parent_educmaster's degree                       7.279615   6.524814
## gendermale:parent_educsome college                         -4.141922   3.991004
## gendermale:parent_educsome high school                      1.008352   3.920233
## gendermale:lunch_typestandard                              -1.073739   2.722340
## gendermale:test_prepnone                                    0.251653   2.713118
## gendermale:parent_marital_statusmarried                    -0.523193   3.867655
## gendermale:parent_marital_statussingle                     -1.745302   4.384747
## gendermale:parent_marital_statuswidowed                     1.627846  18.986441
## gendermale:practice_sportregularly                         -4.310235   4.610325
## gendermale:practice_sportsometimes                         -3.516087   4.634508
## gendermale:is_first_childyes                                3.360372   2.847909
## gendermale:transport_meansschool_bus                       -0.351231   2.632552
## gendermale:wkly_study_hours> 10                            -4.536157   4.129918
## gendermale:wkly_study_hours10-May                          -1.585990   3.132127
## ethnic_groupgroup B:parent_educbachelor's degree           -3.324954  12.924044
## ethnic_groupgroup C:parent_educbachelor's degree           -1.783597  12.903276
## ethnic_groupgroup D:parent_educbachelor's degree           -4.193155  12.805839
## ethnic_groupgroup E:parent_educbachelor's degree          -11.352581  14.573901
## ethnic_groupgroup B:parent_educhigh school                -15.455925   8.091351
## ethnic_groupgroup C:parent_educhigh school                 -8.942855   7.776991
## ethnic_groupgroup D:parent_educhigh school                 -7.859495   7.906714
## ethnic_groupgroup E:parent_educhigh school                 -9.368700   8.805485
## ethnic_groupgroup B:parent_educmaster's degree             19.405920  15.527488
## ethnic_groupgroup C:parent_educmaster's degree              4.673731  14.422492
## ethnic_groupgroup D:parent_educmaster's degree             12.168775  14.651954
## ethnic_groupgroup E:parent_educmaster's degree             14.049007  15.416565
## ethnic_groupgroup B:parent_educsome college                 4.664900   8.948253
## ethnic_groupgroup C:parent_educsome college                 8.349426   8.446297
## ethnic_groupgroup D:parent_educsome college                11.079460   8.797228
## ethnic_groupgroup E:parent_educsome college                 8.211551   8.893668
## ethnic_groupgroup B:parent_educsome high school           -11.966506   8.576569
## ethnic_groupgroup C:parent_educsome high school            -4.495760   8.047085
## ethnic_groupgroup D:parent_educsome high school            -3.780939   8.099992
## ethnic_groupgroup E:parent_educsome high school             4.417092   8.696931
## ethnic_groupgroup B:lunch_typestandard                      5.652071   5.760897
## ethnic_groupgroup C:lunch_typestandard                     10.226437   5.587239
## ethnic_groupgroup D:lunch_typestandard                      8.972876   5.499776
## ethnic_groupgroup E:lunch_typestandard                      1.828807   6.373559
## ethnic_groupgroup B:test_prepnone                           5.358082   5.877498
## ethnic_groupgroup C:test_prepnone                          10.226148   5.513504
## ethnic_groupgroup D:test_prepnone                           7.509603   5.524539
## ethnic_groupgroup E:test_prepnone                          13.877806   6.013663
## ethnic_groupgroup B:parent_marital_statusmarried            7.666966   7.934987
## ethnic_groupgroup C:parent_marital_statusmarried            1.502948   7.306752
## ethnic_groupgroup D:parent_marital_statusmarried           -9.884703   7.206665
## ethnic_groupgroup E:parent_marital_statusmarried           -0.914626   7.973170
## ethnic_groupgroup B:parent_marital_statussingle            18.560281   9.394771
## ethnic_groupgroup C:parent_marital_statussingle             7.986241   8.882343
## ethnic_groupgroup D:parent_marital_statussingle             3.213487   8.582960
## ethnic_groupgroup E:parent_marital_statussingle            14.967904   9.892795
## ethnic_groupgroup B:parent_marital_statuswidowed           50.612530 105.115426
## ethnic_groupgroup C:parent_marital_statuswidowed           78.991045  85.429965
## ethnic_groupgroup D:parent_marital_statuswidowed            4.650894  86.120208
## ethnic_groupgroup E:parent_marital_statuswidowed                  NA         NA
## ethnic_groupgroup B:practice_sportregularly                14.613295  10.525698
## ethnic_groupgroup C:practice_sportregularly                14.627286  10.430812
## ethnic_groupgroup D:practice_sportregularly                12.114331  11.643524
## ethnic_groupgroup E:practice_sportregularly                15.486520  10.659168
## ethnic_groupgroup B:practice_sportsometimes                14.385211  11.228160
## ethnic_groupgroup C:practice_sportsometimes                22.578975  10.921110
## ethnic_groupgroup D:practice_sportsometimes                13.257823  12.039573
## ethnic_groupgroup E:practice_sportsometimes                14.799736  10.976620
## ethnic_groupgroup B:is_first_childyes                       7.019423   5.832717
## ethnic_groupgroup C:is_first_childyes                       0.945600   5.502186
## ethnic_groupgroup D:is_first_childyes                      -0.578091   5.565974
## ethnic_groupgroup E:is_first_childyes                       0.006724   6.269137
## ethnic_groupgroup B:transport_meansschool_bus              -9.549492   5.835934
## ethnic_groupgroup C:transport_meansschool_bus             -12.156811   5.388780
## ethnic_groupgroup D:transport_meansschool_bus              -3.839999   5.383422
## ethnic_groupgroup E:transport_meansschool_bus             -11.722753   6.354914
## ethnic_groupgroup B:wkly_study_hours> 10                   -8.400227   9.935104
## ethnic_groupgroup C:wkly_study_hours> 10                   -0.687654   9.811241
## ethnic_groupgroup D:wkly_study_hours> 10                    0.263262   9.797612
## ethnic_groupgroup E:wkly_study_hours> 10                   -2.759617  10.673194
## ethnic_groupgroup B:wkly_study_hours10-May                 -7.860645   8.344055
## ethnic_groupgroup C:wkly_study_hours10-May                 -2.433650   8.164758
## ethnic_groupgroup D:wkly_study_hours10-May                 -2.347630   8.302701
## ethnic_groupgroup E:wkly_study_hours10-May                 -6.220986   8.939387
## parent_educbachelor's degree:lunch_typestandard             0.537231   5.014512
## parent_educhigh school:lunch_typestandard                   0.798236   4.046623
## parent_educmaster's degree:lunch_typestandard               6.644511   7.416722
## parent_educsome college:lunch_typestandard                  3.328751   4.079308
## parent_educsome high school:lunch_typestandard              5.530921   4.225656
## parent_educbachelor's degree:test_prepnone                 -2.906807   4.626773
## parent_educhigh school:test_prepnone                        2.313360   4.431222
## parent_educmaster's degree:test_prepnone                    0.511485   7.888189
## parent_educsome college:test_prepnone                      -3.095198   4.153258
## parent_educsome high school:test_prepnone                   2.618495   4.016780
## parent_educbachelor's degree:parent_marital_statusmarried -18.253458   8.257834
## parent_educhigh school:parent_marital_statusmarried         3.996656   5.807660
## parent_educmaster's degree:parent_marital_statusmarried     0.758405   8.402414
## parent_educsome college:parent_marital_statusmarried       -7.340772   5.719024
## parent_educsome high school:parent_marital_statusmarried   -4.263094   5.636000
## parent_educbachelor's degree:parent_marital_statussingle  -16.758528   8.901756
## parent_educhigh school:parent_marital_statussingle          8.616682   6.344144
## parent_educmaster's degree:parent_marital_statussingle      0.012577   8.969310
## parent_educsome college:parent_marital_statussingle        -5.727081   6.369453
## parent_educsome high school:parent_marital_statussingle    -1.033222   6.292098
## parent_educbachelor's degree:parent_marital_statuswidowed -21.688307  87.516115
## parent_educhigh school:parent_marital_statuswidowed       -57.550419  96.291731
## parent_educmaster's degree:parent_marital_statuswidowed   -77.367781  50.441787
## parent_educsome college:parent_marital_statuswidowed      -60.045162  63.244771
## parent_educsome high school:parent_marital_statuswidowed  -37.108747  75.801849
## parent_educbachelor's degree:practice_sportregularly       -3.662981   8.525723
## parent_educhigh school:practice_sportregularly            -14.710426   7.337095
## parent_educmaster's degree:practice_sportregularly          1.377177  10.367956
## parent_educsome college:practice_sportregularly            -0.382685   7.461303
## parent_educsome high school:practice_sportregularly        -3.964045   7.205456
## parent_educbachelor's degree:practice_sportsometimes      -12.591005   8.181090
## parent_educhigh school:practice_sportsometimes            -11.930485   6.949111
## parent_educmaster's degree:practice_sportsometimes          6.527368   8.636835
## parent_educsome college:practice_sportsometimes             1.040653   7.180635
## parent_educsome high school:practice_sportsometimes         1.496483   6.751679
## parent_educbachelor's degree:is_first_childyes              4.788458   5.062901
## parent_educhigh school:is_first_childyes                    6.532806   4.321769
## parent_educmaster's degree:is_first_childyes                6.212508   7.559206
## parent_educsome college:is_first_childyes                   9.548352   4.220353
## parent_educsome high school:is_first_childyes               4.792705   4.250326
## parent_educbachelor's degree:transport_meansschool_bus      0.906739   5.054249
## parent_educhigh school:transport_meansschool_bus            3.388782   4.035129
## parent_educmaster's degree:transport_meansschool_bus        4.816803   6.221602
## parent_educsome college:transport_meansschool_bus           3.654650   4.108899
## parent_educsome high school:transport_meansschool_bus       6.032445   4.180954
## parent_educbachelor's degree:wkly_study_hours> 10          -8.191880   7.456993
## parent_educhigh school:wkly_study_hours> 10                -8.343145   6.207418
## parent_educmaster's degree:wkly_study_hours> 10            -1.790263  13.431842
## parent_educsome college:wkly_study_hours> 10               -5.998216   6.248173
## parent_educsome high school:wkly_study_hours> 10           -6.744473   6.363801
## parent_educbachelor's degree:wkly_study_hours10-May        -1.946279   5.182903
## parent_educhigh school:wkly_study_hours10-May             -10.690295   4.832196
## parent_educmaster's degree:wkly_study_hours10-May          -1.124984   6.910172
## parent_educsome college:wkly_study_hours10-May             -2.915727   4.920451
## parent_educsome high school:wkly_study_hours10-May         -8.675554   5.191456
## lunch_typestandard:test_prepnone                           -3.365201   3.035153
## lunch_typestandard:parent_marital_statusmarried            -7.902908   3.971499
## lunch_typestandard:parent_marital_statussingle             -3.707488   4.598623
## lunch_typestandard:parent_marital_statuswidowed             9.372773  78.604395
## lunch_typestandard:practice_sportregularly                  6.988929   5.235054
## lunch_typestandard:practice_sportsometimes                 10.284128   5.046396
## lunch_typestandard:is_first_childyes                       -3.701755   3.075286
## lunch_typestandard:transport_meansschool_bus               -3.696061   2.822109
## lunch_typestandard:wkly_study_hours> 10                     7.910873   4.306472
## lunch_typestandard:wkly_study_hours10-May                  -0.616925   3.221350
## test_prepnone:parent_marital_statusmarried                  3.767046   4.039735
## test_prepnone:parent_marital_statussingle                  -0.269557   4.650957
## test_prepnone:parent_marital_statuswidowed                -33.676919  41.067330
## test_prepnone:practice_sportregularly                       2.975412   5.049660
## test_prepnone:practice_sportsometimes                       4.627924   4.948802
## test_prepnone:is_first_childyes                             1.185331   3.047862
## test_prepnone:transport_meansschool_bus                     1.799887   2.771281
## test_prepnone:wkly_study_hours> 10                         -2.777623   4.350100
## test_prepnone:wkly_study_hours10-May                        1.550628   3.433108
## parent_marital_statusmarried:practice_sportregularly        3.293520   6.491421
## parent_marital_statussingle:practice_sportregularly        -4.424243   8.489011
## parent_marital_statuswidowed:practice_sportregularly       -6.906882  83.123661
## parent_marital_statusmarried:practice_sportsometimes        1.290178   6.401773
## parent_marital_statussingle:practice_sportsometimes        -4.334220   8.299021
## parent_marital_statuswidowed:practice_sportsometimes              NA         NA
## parent_marital_statusmarried:is_first_childyes            -17.146416   4.775198
## parent_marital_statussingle:is_first_childyes              -8.538880   5.292427
## parent_marital_statuswidowed:is_first_childyes             21.917582  29.457760
## parent_marital_statusmarried:transport_meansschool_bus      4.369244   3.943480
## parent_marital_statussingle:transport_meansschool_bus      -1.084605   4.494112
## parent_marital_statuswidowed:transport_meansschool_bus    -14.288412  19.143923
## parent_marital_statusmarried:wkly_study_hours> 10          21.137631   6.160491
## parent_marital_statussingle:wkly_study_hours> 10           27.104463   6.851117
## parent_marital_statuswidowed:wkly_study_hours> 10                 NA         NA
## parent_marital_statusmarried:wkly_study_hours10-May         3.638193   4.522464
## parent_marital_statussingle:wkly_study_hours10-May          4.406511   4.994941
## parent_marital_statuswidowed:wkly_study_hours10-May               NA         NA
## practice_sportregularly:is_first_childyes                  -3.848217   5.864087
## practice_sportsometimes:is_first_childyes                  -6.246496   5.721937
## practice_sportregularly:transport_meansschool_bus           8.897678   4.900075
## practice_sportsometimes:transport_meansschool_bus           5.610130   4.755946
## practice_sportregularly:wkly_study_hours> 10                4.200015   6.947009
## practice_sportsometimes:wkly_study_hours> 10                3.936511   6.813953
## practice_sportregularly:wkly_study_hours10-May              7.801823   5.346218
## practice_sportsometimes:wkly_study_hours10-May              0.374090   5.271160
## is_first_childyes:transport_meansschool_bus                -1.537098   2.982819
## is_first_childyes:wkly_study_hours> 10                      2.206912   4.484172
## is_first_childyes:wkly_study_hours10-May                   -2.954512   3.384923
## transport_meansschool_bus:wkly_study_hours> 10              0.704788   4.309112
## transport_meansschool_bus:wkly_study_hours10-May            2.548938   3.111517
##                                                           t value Pr(>|t|)    
## (Intercept)                                                 4.737 3.06e-06 ***
## gendermale                                                 -1.424 0.155346    
## ethnic_groupgroup B                                        -1.507 0.132711    
## ethnic_groupgroup C                                        -2.145 0.032599 *  
## ethnic_groupgroup D                                        -0.958 0.338510    
## ethnic_groupgroup E                                        -0.866 0.387028    
## parent_educbachelor's degree                                2.127 0.034066 *  
## parent_educhigh school                                      0.823 0.411262    
## parent_educmaster's degree                                 -1.153 0.249476    
## parent_educsome college                                    -0.660 0.509805    
## parent_educsome high school                                -0.364 0.715753    
## lunch_typestandard                                          0.341 0.733134    
## test_prepnone                                              -2.356 0.018974 *  
## parent_marital_statusmarried                                1.395 0.163733    
## parent_marital_statussingle                                 0.369 0.712463    
## parent_marital_statuswidowed                                0.753 0.451919    
## practice_sportregularly                                    -1.624 0.105206    
## practice_sportsometimes                                    -1.429 0.153841    
## is_first_childyes                                           1.646 0.100564    
## transport_meansschool_bus                                  -0.138 0.890518    
## wkly_study_hours> 10                                       -1.319 0.188094    
## wkly_study_hours10-May                                      0.568 0.570177    
## gendermale:ethnic_groupgroup B                              1.430 0.153500    
## gendermale:ethnic_groupgroup C                              2.288 0.022669 *  
## gendermale:ethnic_groupgroup D                              1.548 0.122450    
## gendermale:ethnic_groupgroup E                              1.577 0.115727    
## gendermale:parent_educbachelor's degree                    -0.604 0.546023    
## gendermale:parent_educhigh school                           0.161 0.872488    
## gendermale:parent_educmaster's degree                       1.116 0.265258    
## gendermale:parent_educsome college                         -1.038 0.300011    
## gendermale:parent_educsome high school                      0.257 0.797149    
## gendermale:lunch_typestandard                              -0.394 0.693492    
## gendermale:test_prepnone                                    0.093 0.926147    
## gendermale:parent_marital_statusmarried                    -0.135 0.892466    
## gendermale:parent_marital_statussingle                     -0.398 0.690823    
## gendermale:parent_marital_statuswidowed                     0.086 0.931720    
## gendermale:practice_sportregularly                         -0.935 0.350424    
## gendermale:practice_sportsometimes                         -0.759 0.448513    
## gendermale:is_first_childyes                                1.180 0.238755    
## gendermale:transport_meansschool_bus                       -0.133 0.893933    
## gendermale:wkly_study_hours> 10                            -1.098 0.272735    
## gendermale:wkly_study_hours10-May                          -0.506 0.612894    
## ethnic_groupgroup B:parent_educbachelor's degree           -0.257 0.797109    
## ethnic_groupgroup C:parent_educbachelor's degree           -0.138 0.890133    
## ethnic_groupgroup D:parent_educbachelor's degree           -0.327 0.743513    
## ethnic_groupgroup E:parent_educbachelor's degree           -0.779 0.436480    
## ethnic_groupgroup B:parent_educhigh school                 -1.910 0.056857 .  
## ethnic_groupgroup C:parent_educhigh school                 -1.150 0.250898    
## ethnic_groupgroup D:parent_educhigh school                 -0.994 0.320837    
## ethnic_groupgroup E:parent_educhigh school                 -1.064 0.288016    
## ethnic_groupgroup B:parent_educmaster's degree              1.250 0.212144    
## ethnic_groupgroup C:parent_educmaster's degree              0.324 0.746071    
## ethnic_groupgroup D:parent_educmaster's degree              0.831 0.406761    
## ethnic_groupgroup E:parent_educmaster's degree              0.911 0.362714    
## ethnic_groupgroup B:parent_educsome college                 0.521 0.602445    
## ethnic_groupgroup C:parent_educsome college                 0.989 0.323517    
## ethnic_groupgroup D:parent_educsome college                 1.259 0.208643    
## ethnic_groupgroup E:parent_educsome college                 0.923 0.356431    
## ethnic_groupgroup B:parent_educsome high school            -1.395 0.163747    
## ethnic_groupgroup C:parent_educsome high school            -0.559 0.576705    
## ethnic_groupgroup D:parent_educsome high school            -0.467 0.640921    
## ethnic_groupgroup E:parent_educsome high school             0.508 0.611822    
## ethnic_groupgroup B:lunch_typestandard                      0.981 0.327158    
## ethnic_groupgroup C:lunch_typestandard                      1.830 0.067979 .  
## ethnic_groupgroup D:lunch_typestandard                      1.631 0.103607    
## ethnic_groupgroup E:lunch_typestandard                      0.287 0.774316    
## ethnic_groupgroup B:test_prepnone                           0.912 0.362539    
## ethnic_groupgroup C:test_prepnone                           1.855 0.064401 .  
## ethnic_groupgroup D:test_prepnone                           1.359 0.174846    
## ethnic_groupgroup E:test_prepnone                           2.308 0.021547 *  
## ethnic_groupgroup B:parent_marital_statusmarried            0.966 0.334542    
## ethnic_groupgroup C:parent_marital_statusmarried            0.206 0.837140    
## ethnic_groupgroup D:parent_marital_statusmarried           -1.372 0.170989    
## ethnic_groupgroup E:parent_marital_statusmarried           -0.115 0.908733    
## ethnic_groupgroup B:parent_marital_statussingle             1.976 0.048918 *  
## ethnic_groupgroup C:parent_marital_statussingle             0.899 0.369157    
## ethnic_groupgroup D:parent_marital_statussingle             0.374 0.708312    
## ethnic_groupgroup E:parent_marital_statussingle             1.513 0.131102    
## ethnic_groupgroup B:parent_marital_statuswidowed            0.481 0.630440    
## ethnic_groupgroup C:parent_marital_statuswidowed            0.925 0.355741    
## ethnic_groupgroup D:parent_marital_statuswidowed            0.054 0.956960    
## ethnic_groupgroup E:parent_marital_statuswidowed               NA       NA    
## ethnic_groupgroup B:practice_sportregularly                 1.388 0.165839    
## ethnic_groupgroup C:practice_sportregularly                 1.402 0.161631    
## ethnic_groupgroup D:practice_sportregularly                 1.040 0.298794    
## ethnic_groupgroup E:practice_sportregularly                 1.453 0.147075    
## ethnic_groupgroup B:practice_sportsometimes                 1.281 0.200908    
## ethnic_groupgroup C:practice_sportsometimes                 2.067 0.039362 *  
## ethnic_groupgroup D:practice_sportsometimes                 1.101 0.271507    
## ethnic_groupgroup E:practice_sportsometimes                 1.348 0.178360    
## ethnic_groupgroup B:is_first_childyes                       1.203 0.229543    
## ethnic_groupgroup C:is_first_childyes                       0.172 0.863639    
## ethnic_groupgroup D:is_first_childyes                      -0.104 0.917334    
## ethnic_groupgroup E:is_first_childyes                       0.001 0.999145    
## ethnic_groupgroup B:transport_meansschool_bus              -1.636 0.102593    
## ethnic_groupgroup C:transport_meansschool_bus              -2.256 0.024637 *  
## ethnic_groupgroup D:transport_meansschool_bus              -0.713 0.476094    
## ethnic_groupgroup E:transport_meansschool_bus              -1.845 0.065857 .  
## ethnic_groupgroup B:wkly_study_hours> 10                   -0.846 0.398354    
## ethnic_groupgroup C:wkly_study_hours> 10                   -0.070 0.944160    
## ethnic_groupgroup D:wkly_study_hours> 10                    0.027 0.978577    
## ethnic_groupgroup E:wkly_study_hours> 10                   -0.259 0.796117    
## ethnic_groupgroup B:wkly_study_hours10-May                 -0.942 0.346753    
## ethnic_groupgroup C:wkly_study_hours10-May                 -0.298 0.765813    
## ethnic_groupgroup D:wkly_study_hours10-May                 -0.283 0.777517    
## ethnic_groupgroup E:wkly_study_hours10-May                 -0.696 0.486909    
## parent_educbachelor's degree:lunch_typestandard             0.107 0.914738    
## parent_educhigh school:lunch_typestandard                   0.197 0.843729    
## parent_educmaster's degree:lunch_typestandard               0.896 0.370878    
## parent_educsome college:lunch_typestandard                  0.816 0.415002    
## parent_educsome high school:lunch_typestandard              1.309 0.191356    
## parent_educbachelor's degree:test_prepnone                 -0.628 0.530209    
## parent_educhigh school:test_prepnone                        0.522 0.601931    
## parent_educmaster's degree:test_prepnone                    0.065 0.948334    
## parent_educsome college:test_prepnone                      -0.745 0.456580    
## parent_educsome high school:test_prepnone                   0.652 0.514864    
## parent_educbachelor's degree:parent_marital_statusmarried  -2.210 0.027665 *  
## parent_educhigh school:parent_marital_statusmarried         0.688 0.491762    
## parent_educmaster's degree:parent_marital_statusmarried     0.090 0.928128    
## parent_educsome college:parent_marital_statusmarried       -1.284 0.200068    
## parent_educsome high school:parent_marital_statusmarried   -0.756 0.449872    
## parent_educbachelor's degree:parent_marital_statussingle   -1.883 0.060511 .  
## parent_educhigh school:parent_marital_statussingle          1.358 0.175196    
## parent_educmaster's degree:parent_marital_statussingle      0.001 0.998882    
## parent_educsome college:parent_marital_statussingle        -0.899 0.369139    
## parent_educsome high school:parent_marital_statussingle    -0.164 0.869653    
## parent_educbachelor's degree:parent_marital_statuswidowed  -0.248 0.804406    
## parent_educhigh school:parent_marital_statuswidowed        -0.598 0.550415    
## parent_educmaster's degree:parent_marital_statuswidowed    -1.534 0.125904    
## parent_educsome college:parent_marital_statuswidowed       -0.949 0.343011    
## parent_educsome high school:parent_marital_statuswidowed   -0.490 0.624733    
## parent_educbachelor's degree:practice_sportregularly       -0.430 0.667700    
## parent_educhigh school:practice_sportregularly             -2.005 0.045673 *  
## parent_educmaster's degree:practice_sportregularly          0.133 0.894397    
## parent_educsome college:practice_sportregularly            -0.051 0.959122    
## parent_educsome high school:practice_sportregularly        -0.550 0.582541    
## parent_educbachelor's degree:practice_sportsometimes       -1.539 0.124621    
## parent_educhigh school:practice_sportsometimes             -1.717 0.086818 .  
## parent_educmaster's degree:practice_sportsometimes          0.756 0.450258    
## parent_educsome college:practice_sportsometimes             0.145 0.884846    
## parent_educsome high school:practice_sportsometimes         0.222 0.824708    
## parent_educbachelor's degree:is_first_childyes              0.946 0.344850    
## parent_educhigh school:is_first_childyes                    1.512 0.131459    
## parent_educmaster's degree:is_first_childyes                0.822 0.411676    
## parent_educsome college:is_first_childyes                   2.262 0.024229 *  
## parent_educsome high school:is_first_childyes               1.128 0.260191    
## parent_educbachelor's degree:transport_meansschool_bus      0.179 0.857717    
## parent_educhigh school:transport_meansschool_bus            0.840 0.401533    
## parent_educmaster's degree:transport_meansschool_bus        0.774 0.439287    
## parent_educsome college:transport_meansschool_bus           0.889 0.374321    
## parent_educsome high school:transport_meansschool_bus       1.443 0.149883    
## parent_educbachelor's degree:wkly_study_hours> 10          -1.099 0.272654    
## parent_educhigh school:wkly_study_hours> 10                -1.344 0.179724    
## parent_educmaster's degree:wkly_study_hours> 10            -0.133 0.894038    
## parent_educsome college:wkly_study_hours> 10               -0.960 0.337663    
## parent_educsome high school:wkly_study_hours> 10           -1.060 0.289895    
## parent_educbachelor's degree:wkly_study_hours10-May        -0.376 0.707482    
## parent_educhigh school:wkly_study_hours10-May              -2.212 0.027535 *  
## parent_educmaster's degree:wkly_study_hours10-May          -0.163 0.870761    
## parent_educsome college:wkly_study_hours10-May             -0.593 0.553816    
## parent_educsome high school:wkly_study_hours10-May         -1.671 0.095514 .  
## lunch_typestandard:test_prepnone                           -1.109 0.268237    
## lunch_typestandard:parent_marital_statusmarried            -1.990 0.047312 *  
## lunch_typestandard:parent_marital_statussingle             -0.806 0.420618    
## lunch_typestandard:parent_marital_statuswidowed             0.119 0.905148    
## lunch_typestandard:practice_sportregularly                  1.335 0.182661    
## lunch_typestandard:practice_sportsometimes                  2.038 0.042245 *  
## lunch_typestandard:is_first_childyes                       -1.204 0.229445    
## lunch_typestandard:transport_meansschool_bus               -1.310 0.191089    
## lunch_typestandard:wkly_study_hours> 10                     1.837 0.066989 .  
## lunch_typestandard:wkly_study_hours10-May                  -0.192 0.848226    
## test_prepnone:parent_marital_statusmarried                  0.932 0.351667    
## test_prepnone:parent_marital_statussingle                  -0.058 0.953813    
## test_prepnone:parent_marital_statuswidowed                 -0.820 0.412702    
## test_prepnone:practice_sportregularly                       0.589 0.556054    
## test_prepnone:practice_sportsometimes                       0.935 0.350295    
## test_prepnone:is_first_childyes                             0.389 0.697562    
## test_prepnone:transport_meansschool_bus                     0.649 0.516419    
## test_prepnone:wkly_study_hours> 10                         -0.639 0.523517    
## test_prepnone:wkly_study_hours10-May                        0.452 0.651763    
## parent_marital_statusmarried:practice_sportregularly        0.507 0.612191    
## parent_marital_statussingle:practice_sportregularly        -0.521 0.602548    
## parent_marital_statuswidowed:practice_sportregularly       -0.083 0.933822    
## parent_marital_statusmarried:practice_sportsometimes        0.202 0.840388    
## parent_marital_statussingle:practice_sportsometimes        -0.522 0.601793    
## parent_marital_statuswidowed:practice_sportsometimes           NA       NA    
## parent_marital_statusmarried:is_first_childyes             -3.591 0.000373 ***
## parent_marital_statussingle:is_first_childyes              -1.613 0.107478    
## parent_marital_statuswidowed:is_first_childyes              0.744 0.457312    
## parent_marital_statusmarried:transport_meansschool_bus      1.108 0.268571    
## parent_marital_statussingle:transport_meansschool_bus      -0.241 0.809421    
## parent_marital_statuswidowed:transport_meansschool_bus     -0.746 0.455903    
## parent_marital_statusmarried:wkly_study_hours> 10           3.431 0.000666 ***
## parent_marital_statussingle:wkly_study_hours> 10            3.956 9.07e-05 ***
## parent_marital_statuswidowed:wkly_study_hours> 10              NA       NA    
## parent_marital_statusmarried:wkly_study_hours10-May         0.804 0.421624    
## parent_marital_statussingle:wkly_study_hours10-May          0.882 0.378225    
## parent_marital_statuswidowed:wkly_study_hours10-May            NA       NA    
## practice_sportregularly:is_first_childyes                  -0.656 0.512067    
## practice_sportsometimes:is_first_childyes                  -1.092 0.275662    
## practice_sportregularly:transport_meansschool_bus           1.816 0.070179 .  
## practice_sportsometimes:transport_meansschool_bus           1.180 0.238890    
## practice_sportregularly:wkly_study_hours> 10                0.605 0.545817    
## practice_sportsometimes:wkly_study_hours> 10                0.578 0.563797    
## practice_sportregularly:wkly_study_hours10-May              1.459 0.145298    
## practice_sportsometimes:wkly_study_hours10-May              0.071 0.943459    
## is_first_childyes:transport_meansschool_bus                -0.515 0.606629    
## is_first_childyes:wkly_study_hours> 10                      0.492 0.622891    
## is_first_childyes:wkly_study_hours10-May                   -0.873 0.383295    
## transport_meansschool_bus:wkly_study_hours> 10              0.164 0.870166    
## transport_meansschool_bus:wkly_study_hours10-May            0.819 0.413185    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 12.87 on 383 degrees of freedom
## Multiple R-squared:  0.5303, Adjusted R-squared:  0.2777 
## F-statistic: 2.099 on 206 and 383 DF,  p-value: 2.19e-10
stepwise_model_read <- step(full_fit_read, direction = "both", trace = 1)
## Start:  AIC=3174.13
## reading_score ~ (gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours)^2
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:wkly_study_hours           8     614.8 64084 3163.8
## - parent_educ:wkly_study_hours           10    1420.6 64890 3167.2
## - parent_educ:transport_means             5     415.6 63885 3168.0
## - ethnic_group:parent_educ               20    3769.8 67239 3168.2
## - parent_educ:lunch_type                  5     448.1 63918 3168.3
## - parent_educ:test_prep                   5     452.4 63922 3168.3
## - gender:parent_marital_status            3      36.6 63506 3168.5
## - parent_marital_status:practice_sport    4     295.7 63765 3168.9
## - gender:parent_educ                      5     629.0 64099 3170.0
## - transport_means:wkly_study_hours        2     123.0 63593 3171.3
## - gender:practice_sport                   2     145.0 63615 3171.5
## - test_prep:practice_sport                2     164.3 63634 3171.7
## - ethnic_group:is_first_child             4     609.4 64079 3171.8
## - gender:wkly_study_hours                 2     202.8 63672 3172.0
## - gender:test_prep                        1       1.4 63471 3172.1
## - gender:transport_means                  1       2.9 63473 3172.2
## - test_prep:is_first_child                1      25.1 63495 3172.4
## - gender:lunch_type                       1      25.8 63495 3172.4
## - test_prep:wkly_study_hours              2     242.4 63712 3172.4
## - parent_educ:is_first_child              5     899.0 64369 3172.4
## - is_first_child:transport_means          1      44.0 63514 3172.5
## - practice_sport:is_first_child           2     259.9 63730 3172.5
## - test_prep:transport_means               1      69.9 63539 3172.8
## - is_first_child:wkly_study_hours         2     322.5 63792 3173.1
## - test_prep:parent_marital_status         2     337.8 63807 3173.3
## - parent_educ:parent_marital_status      13    2799.2 66269 3173.6
## - lunch_type:test_prep                    1     203.7 63673 3174.0
## <none>                                                63470 3174.1
## - gender:is_first_child                   1     230.7 63700 3174.3
## - lunch_type:is_first_child               1     240.1 63710 3174.4
## - parent_marital_status:transport_means   3     678.8 64148 3174.4
## - ethnic_group:practice_sport             8    1798.4 65268 3174.6
## - gender:ethnic_group                     4     933.4 64403 3174.7
## - lunch_type:transport_means              1     284.2 63754 3174.8
## - ethnic_group:lunch_type                 4     995.4 64465 3175.3
## - practice_sport:transport_means          2     595.4 64065 3175.6
## - ethnic_group:test_prep                  4    1172.3 64642 3176.9
## - lunch_type:practice_sport               2     753.7 64223 3177.1
## - lunch_type:parent_marital_status        2     780.0 64250 3177.3
## - practice_sport:wkly_study_hours         4    1228.1 64698 3177.4
## - parent_educ:practice_sport             10    2564.7 66034 3177.5
## - lunch_type:wkly_study_hours             2     855.7 64325 3178.0
## - ethnic_group:transport_means            4    1492.9 64962 3179.9
## - ethnic_group:parent_marital_status      9    2935.6 66405 3182.8
## - parent_marital_status:wkly_study_hours  4    2936.1 66406 3192.8
## - parent_marital_status:is_first_child    2    2728.2 66198 3195.0
## 
## Step:  AIC=3163.82
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:parent_educ + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:wkly_study_hours + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:parent_educ               20    3674.5 67759 3156.7
## - parent_educ:transport_means             5     373.1 64458 3157.2
## - parent_marital_status:practice_sport    4     207.2 64292 3157.7
## - parent_educ:test_prep                   5     437.9 64522 3157.8
## - parent_educ:wkly_study_hours           10    1542.6 65627 3157.9
## - parent_educ:lunch_type                  5     440.6 64525 3157.9
## - gender:parent_marital_status            3      40.5 64125 3158.2
## - gender:parent_educ                      5     657.6 64742 3159.8
## - transport_means:wkly_study_hours        2      68.6 64153 3160.5
## - gender:wkly_study_hours                 2     148.7 64233 3161.2
## - gender:practice_sport                   2     163.3 64248 3161.3
## - ethnic_group:is_first_child             4     606.3 64691 3161.4
## - test_prep:practice_sport                2     177.1 64261 3161.4
## - gender:transport_means                  1       1.5 64086 3161.8
## - parent_educ:parent_marital_status      13    2664.0 66748 3161.9
## - test_prep:is_first_child                1      10.1 64094 3161.9
## - gender:test_prep                        1      11.1 64095 3161.9
## - gender:lunch_type                       1      32.7 64117 3162.1
## - test_prep:wkly_study_hours              2     253.0 64337 3162.1
## - parent_educ:is_first_child              5     914.6 64999 3162.2
## - is_first_child:transport_means          1      51.4 64136 3162.3
## - practice_sport:is_first_child           2     272.2 64357 3162.3
## - test_prep:transport_means               1      62.9 64147 3162.4
## - test_prep:parent_marital_status         2     349.0 64433 3163.0
## - lunch_type:test_prep                    1     162.2 64247 3163.3
## - is_first_child:wkly_study_hours         2     382.1 64467 3163.3
## - gender:is_first_child                   1     171.5 64256 3163.4
## <none>                                                64084 3163.8
## - gender:ethnic_group                     4     876.2 64961 3163.8
## - ethnic_group:practice_sport             8    1783.4 65868 3164.0
## - lunch_type:is_first_child               1     255.0 64339 3164.2
## - lunch_type:transport_means              1     257.3 64342 3164.2
## - parent_marital_status:transport_means   3     747.2 64832 3164.7
## - practice_sport:transport_means          2     575.9 64660 3165.1
## - ethnic_group:lunch_type                 4    1030.9 65115 3165.2
## - parent_educ:practice_sport             10    2521.2 66606 3166.6
## - lunch_type:practice_sport               2     747.6 64832 3166.7
## - lunch_type:parent_marital_status        2     764.2 64849 3166.8
## - ethnic_group:test_prep                  4    1220.5 65305 3167.0
## - practice_sport:wkly_study_hours         4    1277.6 65362 3167.5
## - lunch_type:wkly_study_hours             2     896.1 64981 3168.0
## - ethnic_group:transport_means            4    1568.2 65653 3170.1
## - ethnic_group:parent_marital_status      9    2898.4 66983 3171.9
## + ethnic_group:wkly_study_hours           8     614.8 63470 3174.1
## - parent_marital_status:wkly_study_hours  4    2786.9 66871 3180.9
## - parent_marital_status:is_first_child    2    2661.3 66746 3183.8
## 
## Step:  AIC=3156.72
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     parent_educ:wkly_study_hours + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:wkly_study_hours           10    1269.9 69029 3147.7
## - parent_educ:test_prep                   5     307.0 68066 3149.4
## - parent_educ:lunch_type                  5     386.5 68145 3150.1
## - parent_educ:transport_means             5     461.7 68221 3150.7
## - parent_marital_status:practice_sport    4     242.6 68001 3150.8
## - gender:parent_marital_status            3     138.7 67898 3151.9
## - ethnic_group:practice_sport             8    1348.4 69107 3152.3
## - gender:parent_educ                      5     701.3 68460 3152.8
## - parent_educ:is_first_child              5     840.6 68600 3154.0
## - transport_means:wkly_study_hours        2     158.4 67917 3154.1
## - test_prep:practice_sport                2     181.0 67940 3154.3
## - gender:wkly_study_hours                 2     187.1 67946 3154.3
## - is_first_child:wkly_study_hours         2     193.0 67952 3154.4
## - practice_sport:is_first_child           2     209.8 67969 3154.5
## - parent_educ:practice_sport             10    2091.0 69850 3154.6
## - test_prep:is_first_child                1       0.0 67759 3154.7
## - gender:lunch_type                       1       1.5 67760 3154.7
## - gender:transport_means                  1       6.0 67765 3154.8
## - gender:test_prep                        1      28.8 67788 3155.0
## - is_first_child:transport_means          1      31.9 67791 3155.0
## - lunch_type:test_prep                    1      39.0 67798 3155.1
## - gender:is_first_child                   1      53.7 67813 3155.2
## - gender:practice_sport                   2     289.5 68048 3155.2
## - parent_marital_status:transport_means   3     527.4 68286 3155.3
## - test_prep:wkly_study_hours              2     299.0 68058 3155.3
## - lunch_type:parent_marital_status        2     301.2 68060 3155.3
## - ethnic_group:is_first_child             4     776.5 68535 3155.4
## - test_prep:transport_means               1      93.8 67853 3155.5
## - test_prep:parent_marital_status         2     332.4 68091 3155.6
## - parent_educ:parent_marital_status      13    2982.5 70741 3156.1
## - gender:ethnic_group                     4     905.4 68664 3156.5
## - practice_sport:transport_means          2     445.2 68204 3156.6
## <none>                                                67759 3156.7
## - lunch_type:is_first_child               1     315.4 68074 3157.5
## - lunch_type:transport_means              1     316.6 68076 3157.5
## - ethnic_group:test_prep                  4    1135.3 68894 3158.5
## - ethnic_group:lunch_type                 4    1174.9 68934 3158.9
## - practice_sport:wkly_study_hours         4    1254.5 69013 3159.5
## - lunch_type:practice_sport               2     898.1 68657 3160.5
## - ethnic_group:transport_means            4    1420.9 69180 3161.0
## - lunch_type:wkly_study_hours             2    1153.6 68912 3162.7
## + ethnic_group:parent_educ               20    3674.5 64084 3163.8
## - ethnic_group:parent_marital_status      9    2958.5 70717 3163.9
## - parent_marital_status:wkly_study_hours  4    2214.9 69974 3167.7
## + ethnic_group:wkly_study_hours           8     519.5 67239 3168.2
## - parent_marital_status:is_first_child    2    2405.1 70164 3173.3
## 
## Step:  AIC=3147.67
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:lunch_type + parent_educ:test_prep + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:lunch_type                  5     320.2 69349 3140.4
## - parent_educ:test_prep                   5     383.5 69412 3140.9
## - parent_marital_status:practice_sport    4     281.9 69311 3142.1
## - parent_educ:transport_means             5     536.0 69565 3142.2
## - gender:parent_marital_status            3     108.9 69138 3142.6
## - ethnic_group:practice_sport             8    1371.2 70400 3143.3
## - gender:parent_educ                      5     719.3 69748 3143.8
## - parent_educ:is_first_child              5     751.8 69781 3144.1
## - is_first_child:wkly_study_hours         2     140.8 69170 3144.9
## - transport_means:wkly_study_hours        2     190.3 69219 3145.3
## - practice_sport:is_first_child           2     196.8 69226 3145.4
## - test_prep:practice_sport                2     233.3 69262 3145.7
## - test_prep:is_first_child                1       0.2 69029 3145.7
## - gender:transport_means                  1       0.3 69029 3145.7
## - gender:lunch_type                       1       3.0 69032 3145.7
## - gender:practice_sport                   2     243.8 69273 3145.8
## - lunch_type:test_prep                    1      17.2 69046 3145.8
## - gender:test_prep                        1      29.3 69058 3145.9
## - is_first_child:transport_means          1      45.0 69074 3146.1
## - gender:is_first_child                   1      76.7 69106 3146.3
## - gender:wkly_study_hours                 2     313.2 69342 3146.3
## - parent_marital_status:transport_means   3     553.7 69582 3146.4
## - test_prep:parent_marital_status         2     325.4 69354 3146.4
## - test_prep:transport_means               1      96.8 69126 3146.5
## - lunch_type:parent_marital_status        2     332.8 69362 3146.5
## - practice_sport:transport_means          2     339.7 69369 3146.6
## - ethnic_group:is_first_child             4     835.0 69864 3146.8
## - test_prep:wkly_study_hours              2     400.0 69429 3147.1
## - gender:ethnic_group                     4     886.0 69915 3147.2
## - parent_educ:practice_sport             10    2344.8 71374 3147.4
## <none>                                                69029 3147.7
## - lunch_type:is_first_child               1     244.1 69273 3147.8
## - ethnic_group:lunch_type                 4     956.4 69985 3147.8
## - practice_sport:wkly_study_hours         4    1068.0 70097 3148.7
## - lunch_type:transport_means              1     366.9 69396 3148.8
## - parent_educ:parent_marital_status      13    3281.5 72310 3149.1
## - ethnic_group:test_prep                  4    1108.8 70138 3149.1
## - lunch_type:practice_sport               2     846.3 69875 3150.9
## - ethnic_group:transport_means            4    1324.6 70353 3150.9
## - lunch_type:wkly_study_hours             2    1037.5 70066 3152.5
## - ethnic_group:parent_marital_status      9    3215.7 72244 3156.5
## + parent_educ:wkly_study_hours           10    1269.9 67759 3156.7
## + ethnic_group:parent_educ               20    3401.8 65627 3157.9
## + ethnic_group:wkly_study_hours           8     590.3 68439 3158.6
## - parent_marital_status:wkly_study_hours  4    2375.7 71404 3159.6
## - parent_marital_status:is_first_child    2    2553.3 71582 3165.1
## 
## Step:  AIC=3140.4
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:test_prep + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:test_prep                   5     341.0 69690 3133.3
## - parent_marital_status:practice_sport    4     306.4 69655 3135.0
## - parent_educ:transport_means             5     558.5 69908 3135.1
## - ethnic_group:practice_sport             8    1291.4 70640 3135.3
## - gender:parent_marital_status            3     130.7 69480 3135.5
## - gender:parent_educ                      5     692.2 70041 3136.3
## - parent_educ:is_first_child              5     738.5 70088 3136.7
## - is_first_child:wkly_study_hours         2     148.9 69498 3137.7
## - practice_sport:is_first_child           2     212.5 69561 3138.2
## - transport_means:wkly_study_hours        2     223.6 69573 3138.3
## - gender:transport_means                  1       0.1 69349 3138.4
## - test_prep:is_first_child                1       1.4 69350 3138.4
## - gender:practice_sport                   2     240.3 69589 3138.4
## - gender:lunch_type                       1      11.3 69360 3138.5
## - lunch_type:test_prep                    1      17.1 69366 3138.6
## - test_prep:practice_sport                2     258.3 69607 3138.6
## - gender:test_prep                        1      32.6 69382 3138.7
## - is_first_child:transport_means          1      42.2 69391 3138.8
## - gender:wkly_study_hours                 2     292.4 69641 3138.9
## - lunch_type:parent_marital_status        2     322.6 69672 3139.1
## - test_prep:parent_marital_status         2     339.4 69688 3139.3
## - test_prep:transport_means               1     110.2 69459 3139.3
## - gender:is_first_child                   1     123.4 69472 3139.4
## - parent_marital_status:transport_means   3     609.9 69959 3139.6
## - ethnic_group:is_first_child             4     848.6 70198 3139.6
## - gender:ethnic_group                     4     857.9 70207 3139.7
## - test_prep:wkly_study_hours              2     403.6 69753 3139.8
## - practice_sport:transport_means          2     407.8 69757 3139.9
## - lunch_type:is_first_child               1     218.0 69567 3140.3
## <none>                                                69349 3140.4
## - ethnic_group:lunch_type                 4     951.4 70300 3140.4
## - parent_educ:practice_sport             10    2413.6 71763 3140.6
## - lunch_type:transport_means              1     377.6 69727 3141.6
## - practice_sport:wkly_study_hours         4    1124.5 70474 3141.9
## - ethnic_group:test_prep                  4    1131.5 70481 3141.9
## - parent_educ:parent_marital_status      13    3369.7 72719 3142.4
## - lunch_type:practice_sport               2     809.1 70158 3143.2
## - ethnic_group:transport_means            4    1299.6 70649 3143.4
## - lunch_type:wkly_study_hours             2     993.1 70342 3144.8
## + parent_educ:lunch_type                  5     320.2 69029 3147.7
## - ethnic_group:parent_marital_status      9    3147.4 72496 3148.6
## + parent_educ:wkly_study_hours           10    1203.6 68145 3150.1
## + ethnic_group:parent_educ               20    3421.3 65928 3150.6
## + ethnic_group:wkly_study_hours           8     565.0 68784 3151.6
## - parent_marital_status:wkly_study_hours  4    2520.8 71870 3153.5
## - parent_marital_status:is_first_child    2    2752.7 72102 3159.4
## 
## Step:  AIC=3133.3
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:practice_sport + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:is_first_child + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_marital_status:practice_sport    4     317.6 70008 3128.0
## - ethnic_group:practice_sport             8    1274.2 70964 3128.0
## - gender:parent_marital_status            3     123.8 69814 3128.3
## - gender:parent_educ                      5     652.4 70342 3128.8
## - parent_educ:transport_means             5     667.2 70357 3128.9
## - parent_educ:is_first_child              5     796.7 70487 3130.0
## - is_first_child:wkly_study_hours         2     124.6 69815 3130.3
## - practice_sport:is_first_child           2     200.9 69891 3131.0
## - transport_means:wkly_study_hours        2     208.5 69899 3131.1
## - gender:practice_sport                   2     223.7 69914 3131.2
## - test_prep:practice_sport                2     229.3 69919 3131.2
## - test_prep:is_first_child                1       0.3 69690 3131.3
## - gender:transport_means                  1       1.0 69691 3131.3
## - gender:lunch_type                       1       8.7 69699 3131.4
## - lunch_type:test_prep                    1      19.1 69709 3131.5
## - lunch_type:parent_marital_status        2     264.9 69955 3131.5
## - gender:ethnic_group                     4     753.5 70444 3131.6
## - gender:test_prep                        1      55.9 69746 3131.8
## - test_prep:parent_marital_status         2     301.2 69991 3131.8
## - is_first_child:transport_means          1      67.9 69758 3131.9
## - gender:wkly_study_hours                 2     310.5 70001 3131.9
## - test_prep:transport_means               1     100.3 69790 3132.2
## - gender:is_first_child                   1     104.9 69795 3132.2
## - parent_marital_status:transport_means   3     587.6 70278 3132.2
## - ethnic_group:is_first_child             4     907.0 70597 3132.9
## - practice_sport:transport_means          2     436.3 70126 3133.0
## - test_prep:wkly_study_hours              2     443.2 70133 3133.0
## <none>                                                69690 3133.3
## - ethnic_group:test_prep                  4     951.6 70642 3133.3
## - lunch_type:is_first_child               1     248.8 69939 3133.4
## - parent_educ:practice_sport             10    2425.2 72115 3133.5
## - ethnic_group:lunch_type                 4    1002.5 70692 3133.7
## - lunch_type:transport_means              1     375.0 70065 3134.5
## - parent_educ:parent_marital_status      13    3343.7 73034 3134.9
## - practice_sport:wkly_study_hours         4    1153.2 70843 3135.0
## - ethnic_group:transport_means            4    1310.7 71001 3136.3
## - lunch_type:practice_sport               2     917.5 70608 3137.0
## - lunch_type:wkly_study_hours             2    1061.6 70752 3138.2
## + parent_educ:test_prep                   5     341.0 69349 3140.4
## - ethnic_group:parent_marital_status      9    3065.0 72755 3140.7
## + parent_educ:lunch_type                  5     277.8 69412 3140.9
## + parent_educ:wkly_study_hours           10    1255.7 68434 3142.6
## + ethnic_group:wkly_study_hours           8     565.8 69124 3144.5
## + ethnic_group:parent_educ               20    3212.4 66478 3145.4
## - parent_marital_status:wkly_study_hours  4    2684.2 72374 3147.6
## - parent_marital_status:is_first_child    2    2781.2 72471 3152.4
## 
## Step:  AIC=3127.98
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:parent_marital_status + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:practice_sport + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:parent_marital_status            3     122.7 70130 3123.0
## - ethnic_group:practice_sport             8    1365.0 71373 3123.4
## - gender:parent_educ                      5     663.1 70671 3123.5
## - parent_educ:transport_means             5     690.2 70698 3123.8
## - lunch_type:parent_marital_status        3     322.0 70330 3124.7
## - parent_educ:is_first_child              5     800.9 70809 3124.7
## - practice_sport:is_first_child           2     150.9 70159 3125.2
## - is_first_child:wkly_study_hours         2     163.9 70172 3125.4
## - transport_means:wkly_study_hours        2     204.8 70212 3125.7
## - test_prep:practice_sport                2     236.5 70244 3126.0
## - gender:ethnic_group                     4     714.8 70722 3126.0
## - test_prep:is_first_child                1       0.6 70008 3126.0
## - gender:transport_means                  1       1.9 70010 3126.0
## - gender:lunch_type                       1       7.2 70015 3126.0
## - lunch_type:test_prep                    1      18.2 70026 3126.1
## - gender:practice_sport                   2     264.3 70272 3126.2
## - test_prep:parent_marital_status         2     280.5 70288 3126.3
## - gender:test_prep                        1      66.7 70074 3126.5
## - is_first_child:transport_means          1      87.2 70095 3126.7
## - test_prep:transport_means               1      93.7 70101 3126.8
## - gender:is_first_child                   1      97.3 70105 3126.8
## - gender:wkly_study_hours                 2     342.9 70351 3126.9
## - parent_marital_status:transport_means   3     583.7 70591 3126.9
## - practice_sport:transport_means          2     401.2 70409 3127.3
## - lunch_type:is_first_child               1     177.5 70185 3127.5
## - ethnic_group:is_first_child             4     929.5 70937 3127.8
## - ethnic_group:test_prep                  4     940.7 70948 3127.9
## - test_prep:wkly_study_hours              2     463.2 70471 3127.9
## <none>                                                70008 3128.0
## - parent_educ:practice_sport             10    2449.6 72457 3128.3
## - lunch_type:transport_means              1     337.8 70345 3128.8
## - parent_educ:parent_marital_status      14    3565.4 73573 3129.3
## - ethnic_group:lunch_type                 4    1115.6 71123 3129.3
## - practice_sport:wkly_study_hours         4    1150.0 71158 3129.6
## - ethnic_group:transport_means            4    1283.9 71292 3130.7
## - lunch_type:practice_sport               2     877.2 70885 3131.3
## - lunch_type:wkly_study_hours             2    1099.1 71107 3133.2
## + parent_marital_status:practice_sport    4     317.6 69690 3133.3
## - ethnic_group:parent_marital_status     10    3190.9 73199 3134.3
## + parent_educ:test_prep                   5     352.3 69655 3135.0
## + parent_educ:lunch_type                  5     297.6 69710 3135.5
## + parent_educ:wkly_study_hours           10    1290.0 68718 3137.0
## + ethnic_group:wkly_study_hours           8     481.0 69527 3139.9
## + ethnic_group:parent_educ               20    3249.9 66758 3139.9
## - parent_marital_status:wkly_study_hours  5    2853.2 72861 3141.6
## - parent_marital_status:is_first_child    2    3039.8 73048 3149.1
## 
## Step:  AIC=3123.01
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:practice_sport + gender:is_first_child + gender:transport_means + 
##     gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:parent_marital_status + ethnic_group:practice_sport + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + parent_educ:transport_means + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:practice_sport             8    1356.7 71487 3118.3
## - gender:parent_educ                      5     677.1 70808 3118.7
## - parent_educ:transport_means             5     685.0 70815 3118.8
## - parent_educ:is_first_child              5     819.9 70950 3119.9
## - lunch_type:parent_marital_status        3     369.0 70499 3120.1
## - practice_sport:is_first_child           2     144.7 70275 3120.2
## - is_first_child:wkly_study_hours         2     152.6 70283 3120.3
## - transport_means:wkly_study_hours        2     204.9 70335 3120.7
## - gender:ethnic_group                     4     700.0 70830 3120.9
## - test_prep:is_first_child                1       0.5 70131 3121.0
## - gender:transport_means                  1       1.0 70131 3121.0
## - gender:lunch_type                       1       4.8 70135 3121.1
## - lunch_type:test_prep                    1      21.6 70152 3121.2
## - test_prep:practice_sport                2     266.1 70396 3121.2
## - gender:practice_sport                   2     277.7 70408 3121.3
## - test_prep:parent_marital_status         2     280.8 70411 3121.4
## - gender:test_prep                        1      80.0 70210 3121.7
## - test_prep:transport_means               1      91.3 70222 3121.8
## - is_first_child:transport_means          1     113.9 70244 3122.0
## - gender:is_first_child                   1     114.3 70245 3122.0
## - gender:wkly_study_hours                 2     363.0 70493 3122.1
## - practice_sport:transport_means          2     389.5 70520 3122.3
## - parent_marital_status:transport_means   3     660.2 70791 3122.5
## - lunch_type:is_first_child               1     183.4 70314 3122.6
## - ethnic_group:is_first_child             4     913.5 71044 3122.7
## - test_prep:wkly_study_hours              2     455.4 70586 3122.8
## - ethnic_group:test_prep                  4     952.9 71083 3123.0
## <none>                                                70130 3123.0
## - parent_educ:parent_marital_status      14    3455.4 73586 3123.4
## - lunch_type:transport_means              1     356.3 70487 3124.0
## - ethnic_group:lunch_type                 4    1108.7 71239 3124.3
## - parent_educ:practice_sport             10    2585.2 72716 3124.4
## - practice_sport:wkly_study_hours         4    1194.7 71325 3125.0
## - ethnic_group:transport_means            4    1264.1 71395 3125.6
## - lunch_type:practice_sport               2     959.8 71090 3127.0
## + gender:parent_marital_status            3     122.7 70008 3128.0
## - lunch_type:wkly_study_hours             2    1110.6 71241 3128.3
## + parent_marital_status:practice_sport    4     316.5 69814 3128.3
## - ethnic_group:parent_marital_status     10    3250.3 73381 3129.7
## + parent_educ:test_prep                   5     345.4 69785 3130.1
## + parent_educ:lunch_type                  5     315.8 69815 3130.3
## + parent_educ:wkly_study_hours           10    1252.2 68878 3132.4
## + ethnic_group:parent_educ               20    3339.0 66791 3134.2
## + ethnic_group:wkly_study_hours           8     511.2 69619 3134.7
## - parent_marital_status:wkly_study_hours  5    2844.3 72975 3136.5
## - parent_marital_status:is_first_child    2    3138.1 73269 3144.8
## 
## Step:  AIC=3118.32
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:practice_sport + gender:is_first_child + gender:transport_means + 
##     gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:transport_means             5     548.5 72036 3112.8
## - gender:parent_educ                      5     581.6 72069 3113.1
## - gender:ethnic_group                     4     534.8 72022 3114.7
## - practice_sport:is_first_child           2     121.8 71609 3115.3
## - lunch_type:parent_marital_status        3     394.4 71882 3115.6
## - is_first_child:wkly_study_hours         2     177.5 71665 3115.8
## - test_prep:practice_sport                2     196.3 71683 3115.9
## - parent_educ:is_first_child              5     939.4 72427 3116.0
## - transport_means:wkly_study_hours        2     221.2 71708 3116.1
## - lunch_type:test_prep                    1       0.0 71487 3116.3
## - gender:lunch_type                       1       0.1 71487 3116.3
## - gender:transport_means                  1       0.3 71487 3116.3
## - test_prep:is_first_child                1       0.7 71488 3116.3
## - gender:test_prep                        1      50.9 71538 3116.7
## - gender:is_first_child                   1      53.6 71541 3116.8
## - test_prep:parent_marital_status         2     313.1 71800 3116.9
## - ethnic_group:is_first_child             4     825.4 72313 3117.1
## - test_prep:wkly_study_hours              2     338.3 71825 3117.1
## - test_prep:transport_means               1     106.9 71594 3117.2
## - practice_sport:transport_means          2     376.1 71863 3117.4
## - is_first_child:transport_means          1     164.3 71651 3117.7
## - ethnic_group:test_prep                  4     919.2 72406 3117.9
## - gender:practice_sport                   2     453.1 71940 3118.1
## <none>                                                71487 3118.3
## - gender:wkly_study_hours                 2     487.4 71974 3118.3
## - lunch_type:is_first_child               1     245.8 71733 3118.3
## - lunch_type:transport_means              1     258.5 71746 3118.4
## - parent_educ:parent_marital_status      14    3522.4 75010 3118.7
## - parent_marital_status:transport_means   3     781.1 72268 3118.7
## - parent_educ:practice_sport             10    2650.7 74138 3119.8
## - practice_sport:wkly_study_hours         4    1180.8 72668 3120.0
## - ethnic_group:lunch_type                 4    1274.7 72762 3120.8
## - ethnic_group:transport_means            4    1324.6 72812 3121.2
## - lunch_type:practice_sport               2     969.1 72456 3122.3
## + parent_marital_status:practice_sport    4     402.2 71085 3123.0
## + ethnic_group:practice_sport             8    1356.7 70130 3123.0
## - lunch_type:wkly_study_hours             2    1089.7 72577 3123.2
## + gender:parent_marital_status            3     114.4 71373 3123.4
## - ethnic_group:parent_marital_status     10    3370.4 74858 3125.5
## + parent_educ:test_prep                   5     312.5 71175 3125.7
## + parent_educ:lunch_type                  5     224.8 71262 3126.5
## + parent_educ:wkly_study_hours           10    1304.6 70182 3127.4
## + ethnic_group:wkly_study_hours           8     473.3 71014 3130.4
## - parent_marital_status:wkly_study_hours  5    2938.9 74426 3132.1
## + ethnic_group:parent_educ               20    2867.8 68619 3134.2
## - parent_marital_status:is_first_child    2    2933.5 74421 3138.1
## 
## Step:  AIC=3112.83
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:parent_educ + gender:lunch_type + gender:test_prep + 
##     gender:practice_sport + gender:is_first_child + gender:transport_means + 
##     gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + parent_educ:is_first_child + 
##     lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:parent_educ                      5     603.8 72639 3107.8
## - gender:ethnic_group                     4     475.9 72512 3108.7
## - practice_sport:is_first_child           2      88.0 72124 3109.6
## - is_first_child:wkly_study_hours         2     178.3 72214 3110.3
## - test_prep:practice_sport                2     197.3 72233 3110.4
## - lunch_type:parent_marital_status        3     454.7 72490 3110.5
## - parent_educ:is_first_child              5     958.0 72994 3110.6
## - transport_means:wkly_study_hours        2     234.3 72270 3110.7
## - gender:transport_means                  1       0.0 72036 3110.8
## - test_prep:is_first_child                1       0.9 72036 3110.8
## - gender:lunch_type                       1       1.7 72037 3110.8
## - lunch_type:test_prep                    1       2.7 72038 3110.8
## - gender:test_prep                        1      37.7 72073 3111.1
## - test_prep:parent_marital_status         2     287.2 72323 3111.2
## - gender:is_first_child                   1      49.1 72085 3111.2
## - practice_sport:transport_means          2     304.8 72340 3111.3
## - test_prep:wkly_study_hours              2     352.0 72388 3111.7
## - is_first_child:transport_means          1     135.0 72171 3111.9
## - ethnic_group:is_first_child             4     874.0 72910 3111.9
## - test_prep:transport_means               1     146.1 72182 3112.0
## - parent_marital_status:transport_means   3     668.1 72704 3112.3
## - gender:wkly_study_hours                 2     433.5 72469 3112.4
## - parent_educ:parent_marital_status      14    3444.3 75480 3112.4
## - ethnic_group:test_prep                  4     945.8 72981 3112.5
## - gender:practice_sport                   2     458.7 72494 3112.6
## - lunch_type:is_first_child               1     235.4 72271 3112.8
## <none>                                                72036 3112.8
## - lunch_type:transport_means              1     251.0 72287 3112.9
## - parent_educ:practice_sport             10    2633.4 74669 3114.0
## - practice_sport:wkly_study_hours         4    1297.2 73333 3115.4
## - ethnic_group:lunch_type                 4    1387.9 73424 3116.1
## - ethnic_group:transport_means            4    1456.2 73492 3116.6
## - lunch_type:practice_sport               2     986.4 73022 3116.8
## + parent_marital_status:practice_sport    4     414.6 71621 3117.4
## + gender:parent_marital_status            3     109.2 71926 3117.9
## + parent_educ:transport_means             5     548.5 71487 3118.3
## - lunch_type:wkly_study_hours             2    1169.8 73205 3118.3
## + ethnic_group:practice_sport             8    1220.2 70815 3118.8
## + parent_educ:test_prep                   5     395.4 71640 3119.6
## - ethnic_group:parent_marital_status     10    3435.4 75471 3120.3
## + parent_educ:lunch_type                  5     241.7 71794 3120.8
## + parent_educ:wkly_study_hours           10    1335.5 70700 3121.8
## + ethnic_group:wkly_study_hours           8     495.2 71540 3124.8
## - parent_marital_status:wkly_study_hours  5    3004.4 75040 3126.9
## + ethnic_group:parent_educ               20    3017.4 69018 3127.6
## - parent_marital_status:is_first_child    2    2981.2 75017 3132.8
## 
## Step:  AIC=3107.75
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:ethnic_group + 
##     gender:lunch_type + gender:test_prep + gender:practice_sport + 
##     gender:is_first_child + gender:transport_means + gender:wkly_study_hours + 
##     ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:ethnic_group                     4     357.5 72997 3102.7
## - parent_educ:is_first_child              5     838.9 73478 3104.5
## - practice_sport:is_first_child           2     105.8 72745 3104.6
## - lunch_type:parent_marital_status        3     422.0 73061 3105.2
## - is_first_child:wkly_study_hours         2     205.4 72845 3105.4
## - transport_means:wkly_study_hours        2     231.0 72870 3105.6
## - gender:transport_means                  1       0.0 72639 3105.8
## - gender:lunch_type                       1       1.4 72641 3105.8
## - test_prep:is_first_child                1       4.8 72644 3105.8
## - lunch_type:test_prep                    1      11.0 72650 3105.8
## - test_prep:practice_sport                2     260.4 72900 3105.9
## - test_prep:parent_marital_status         2     267.3 72907 3105.9
## - gender:test_prep                        1      27.3 72667 3106.0
## - practice_sport:transport_means          2     287.5 72927 3106.1
## - gender:is_first_child                   1      46.8 72686 3106.1
## - ethnic_group:test_prep                  4     856.3 73496 3106.7
## - ethnic_group:is_first_child             4     858.1 73497 3106.7
## - is_first_child:transport_means          1     127.0 72766 3106.8
## - test_prep:transport_means               1     128.8 72768 3106.8
## - test_prep:wkly_study_hours              2     412.9 73052 3107.1
## - gender:wkly_study_hours                 2     454.8 73094 3107.4
## - gender:practice_sport                   2     463.1 73103 3107.5
## - lunch_type:is_first_child               1     216.9 72856 3107.5
## - parent_marital_status:transport_means   3     724.1 73363 3107.6
## <none>                                                72639 3107.8
## - parent_educ:practice_sport             10    2551.6 75191 3108.1
## - lunch_type:transport_means              1     333.5 72973 3108.5
## - parent_educ:parent_marital_status      14    3774.3 76414 3109.6
## - practice_sport:wkly_study_hours         4    1233.1 73872 3109.7
## - ethnic_group:lunch_type                 4    1289.5 73929 3110.1
## - lunch_type:practice_sport               2     942.3 73582 3111.4
## + parent_marital_status:practice_sport    4     431.9 72207 3112.2
## - ethnic_group:transport_means            4    1600.7 74240 3112.6
## + gender:parent_educ                      5     603.8 72036 3112.8
## + gender:parent_marital_status            3     108.8 72531 3112.9
## - lunch_type:wkly_study_hours             2    1157.9 73797 3113.1
## + parent_educ:transport_means             5     570.6 72069 3113.1
## - ethnic_group:parent_marital_status     10    3305.3 75945 3114.0
## + ethnic_group:practice_sport             8    1130.0 71509 3114.5
## + parent_educ:test_prep                   5     351.2 72288 3114.9
## + parent_educ:lunch_type                  5     235.7 72404 3115.8
## + parent_educ:wkly_study_hours           10    1314.3 71325 3117.0
## + ethnic_group:wkly_study_hours           8     515.2 72124 3119.6
## + ethnic_group:parent_educ               20    3119.5 69520 3121.9
## - parent_marital_status:wkly_study_hours  5    3076.4 75716 3122.2
## - parent_marital_status:is_first_child    2    2985.7 75625 3127.5
## 
## Step:  AIC=3102.65
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:is_first_child + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - practice_sport:is_first_child           2     121.5 73118 3099.6
## - lunch_type:parent_marital_status        3     402.0 73399 3099.9
## - is_first_child:wkly_study_hours         2     204.6 73201 3100.3
## - parent_educ:is_first_child              5     960.2 73957 3100.4
## - ethnic_group:test_prep                  4     712.7 73710 3100.4
## - transport_means:wkly_study_hours        2     234.6 73231 3100.5
## - gender:lunch_type                       1       0.3 72997 3100.7
## - gender:transport_means                  1       1.6 72998 3100.7
## - test_prep:parent_marital_status         2     250.2 73247 3100.7
## - test_prep:is_first_child                1       5.9 73003 3100.7
## - test_prep:practice_sport                2     258.1 73255 3100.7
## - lunch_type:test_prep                    1      18.8 73016 3100.8
## - gender:test_prep                        1      19.3 73016 3100.8
## - practice_sport:transport_means          2     282.8 73280 3100.9
## - gender:is_first_child                   1      55.7 73052 3101.1
## - ethnic_group:is_first_child             4     838.1 73835 3101.4
## - test_prep:transport_means               1     135.7 73132 3101.7
## - is_first_child:transport_means          1     147.7 73145 3101.8
## - test_prep:wkly_study_hours              2     417.8 73415 3102.0
## - gender:practice_sport                   2     467.7 73465 3102.4
## - lunch_type:is_first_child               1     223.6 73220 3102.4
## <none>                                                72997 3102.7
## - gender:wkly_study_hours                 2     497.9 73495 3102.7
## - parent_marital_status:transport_means   3     785.6 73782 3103.0
## - parent_educ:practice_sport             10    2563.4 75560 3103.0
## - lunch_type:transport_means              1     326.1 73323 3103.3
## - ethnic_group:lunch_type                 4    1273.0 74270 3104.8
## - practice_sport:wkly_study_hours         4    1285.8 74283 3104.9
## - parent_educ:parent_marital_status      14    3916.8 76914 3105.5
## - lunch_type:practice_sport               2    1063.9 74061 3107.2
## + parent_marital_status:practice_sport    4     401.1 72596 3107.4
## - ethnic_group:transport_means            4    1601.0 74598 3107.4
## - ethnic_group:parent_marital_status     10    3170.2 76167 3107.7
## + gender:ethnic_group                     4     357.5 72639 3107.8
## + gender:parent_marital_status            3     100.5 72896 3107.8
## - lunch_type:wkly_study_hours             2    1180.5 74177 3108.1
## + parent_educ:transport_means             5     515.8 72481 3108.5
## + gender:parent_educ                      5     485.3 72512 3108.7
## + ethnic_group:practice_sport             8    1051.0 71946 3110.1
## + parent_educ:test_prep                   5     256.9 72740 3110.6
## + parent_educ:lunch_type                  5     226.0 72771 3110.8
## + parent_educ:wkly_study_hours           10    1282.6 71714 3112.2
## + ethnic_group:wkly_study_hours           8     491.4 72505 3114.7
## - parent_marital_status:wkly_study_hours  5    3086.2 76083 3117.1
## + ethnic_group:parent_educ               20    3022.3 69974 3117.7
## - parent_marital_status:is_first_child    2    3076.4 76073 3123.0
## 
## Step:  AIC=3099.63
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:parent_marital_status        3     374.8 73493 3096.7
## - is_first_child:wkly_study_hours         2     186.9 73305 3097.1
## - parent_educ:is_first_child              5     949.9 74068 3097.2
## - ethnic_group:test_prep                  4     732.4 73851 3097.5
## - transport_means:wkly_study_hours        2     238.0 73356 3097.6
## - test_prep:parent_marital_status         2     246.9 73365 3097.6
## - gender:lunch_type                       1       0.3 73119 3097.6
## - test_prep:is_first_child                1       1.5 73120 3097.6
## - gender:transport_means                  1       2.9 73121 3097.7
## - lunch_type:test_prep                    1      23.0 73141 3097.8
## - practice_sport:transport_means          2     271.5 73390 3097.8
## - gender:test_prep                        1      24.4 73143 3097.8
## - test_prep:practice_sport                2     282.1 73400 3097.9
## - gender:is_first_child                   1      66.2 73184 3098.2
## - ethnic_group:is_first_child             4     870.1 73988 3098.6
## - test_prep:transport_means               1     138.4 73257 3098.8
## - test_prep:wkly_study_hours              2     402.6 73521 3098.9
## - is_first_child:transport_means          1     164.6 73283 3099.0
## - gender:practice_sport                   2     455.9 73574 3099.3
## - gender:wkly_study_hours                 2     489.8 73608 3099.6
## - lunch_type:is_first_child               1     245.7 73364 3099.6
## - parent_marital_status:transport_means   3     746.7 73865 3099.6
## <none>                                                73118 3099.6
## - parent_educ:practice_sport             10    2528.0 75646 3099.7
## - lunch_type:transport_means              1     326.5 73445 3100.3
## - ethnic_group:lunch_type                 4    1294.0 74412 3102.0
## - parent_educ:parent_marital_status      14    3861.6 76980 3102.0
## - practice_sport:wkly_study_hours         4    1302.5 74421 3102.1
## + practice_sport:is_first_child           2     121.5 72997 3102.7
## - ethnic_group:transport_means            4    1550.5 74669 3104.0
## - lunch_type:practice_sport               2    1065.3 74184 3104.2
## - ethnic_group:parent_marital_status     10    3109.3 76228 3104.2
## + gender:ethnic_group                     4     373.1 72745 3104.6
## + parent_marital_status:practice_sport    4     367.7 72751 3104.7
## + gender:parent_marital_status            3      88.8 73030 3104.9
## - lunch_type:wkly_study_hours             2    1188.6 74307 3105.1
## + gender:parent_educ                      5     501.0 72617 3105.6
## + parent_educ:transport_means             5     474.9 72643 3105.8
## + ethnic_group:practice_sport             8    1036.1 72082 3107.2
## + parent_educ:test_prep                   5     245.0 72873 3107.7
## + parent_educ:lunch_type                  5     228.7 72890 3107.8
## + parent_educ:wkly_study_hours           10    1277.4 71841 3109.2
## + ethnic_group:wkly_study_hours           8     505.9 72612 3111.5
## - parent_marital_status:wkly_study_hours  5    3089.3 76208 3114.1
## + ethnic_group:parent_educ               20    2920.9 70197 3115.6
## - parent_marital_status:is_first_child    2    3028.3 76147 3119.6
## 
## Step:  AIC=3096.65
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:parent_marital_status + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + is_first_child:wkly_study_hours + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:is_first_child              5     908.9 74402 3093.9
## - is_first_child:wkly_study_hours         2     173.4 73667 3094.0
## - test_prep:parent_marital_status         2     234.7 73728 3094.5
## - test_prep:is_first_child                1       1.1 73494 3094.7
## - ethnic_group:test_prep                  4     753.5 74247 3094.7
## - gender:lunch_type                       1       6.4 73500 3094.7
## - gender:transport_means                  1       6.7 73500 3094.7
## - lunch_type:test_prep                    1      20.6 73514 3094.8
## - practice_sport:transport_means          2     273.6 73767 3094.8
## - transport_means:wkly_study_hours        2     274.4 73767 3094.8
## - gender:test_prep                        1      35.5 73529 3094.9
## - test_prep:practice_sport                2     290.9 73784 3095.0
## - ethnic_group:is_first_child             4     829.3 74322 3095.3
## - gender:is_first_child                   1      81.0 73574 3095.3
## - test_prep:transport_means               1     136.1 73629 3095.7
## - test_prep:wkly_study_hours              2     402.3 73895 3095.9
## - gender:practice_sport                   2     412.2 73905 3095.9
## - is_first_child:transport_means          1     175.2 73668 3096.1
## - gender:wkly_study_hours                 2     431.3 73924 3096.1
## - lunch_type:is_first_child               1     218.5 73712 3096.4
## - parent_marital_status:transport_means   3     743.8 74237 3096.6
## <none>                                                73493 3096.7
## - parent_educ:practice_sport             10    2548.8 76042 3096.8
## - lunch_type:transport_means              1     328.3 73821 3097.3
## - practice_sport:wkly_study_hours         4    1295.6 74789 3099.0
## - parent_educ:parent_marital_status      14    3920.7 77414 3099.3
## + lunch_type:parent_marital_status        3     374.8 73118 3099.6
## - ethnic_group:lunch_type                 4    1393.2 74886 3099.7
## + practice_sport:is_first_child           2      94.3 73399 3099.9
## - lunch_type:practice_sport               2     998.0 74491 3100.6
## - ethnic_group:parent_marital_status     10    3049.2 76542 3100.6
## - ethnic_group:transport_means            4    1542.9 75036 3100.9
## - lunch_type:wkly_study_hours             2    1093.4 74587 3101.4
## + gender:parent_marital_status            3     124.4 73369 3101.7
## + gender:ethnic_group                     4     351.9 73141 3101.8
## + parent_educ:transport_means             5     521.3 72972 3102.4
## + gender:parent_educ                      5     479.0 73014 3102.8
## + parent_marital_status:practice_sport    5     428.2 73065 3103.2
## + ethnic_group:practice_sport             8    1039.1 72454 3104.2
## + parent_educ:lunch_type                  5     221.6 73272 3104.9
## + parent_educ:test_prep                   5     214.7 73278 3104.9
## + parent_educ:wkly_study_hours           10    1282.2 72211 3106.3
## + ethnic_group:wkly_study_hours           8     478.5 73015 3108.8
## - parent_marital_status:wkly_study_hours  5    2984.5 76478 3110.1
## + ethnic_group:parent_educ               20    2625.3 70868 3115.2
## - parent_marital_status:is_first_child    2    3010.8 76504 3116.3
## 
## Step:  AIC=3093.9
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     is_first_child:wkly_study_hours + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - is_first_child:wkly_study_hours         2     116.1 74518 3090.8
## - test_prep:parent_marital_status         2     216.2 74618 3091.6
## - test_prep:is_first_child                1       1.0 74403 3091.9
## - gender:transport_means                  1       2.7 74405 3091.9
## - gender:lunch_type                       1       4.7 74407 3091.9
## - transport_means:wkly_study_hours        2     263.8 74666 3092.0
## - ethnic_group:test_prep                  4     772.1 75174 3092.0
## - lunch_type:test_prep                    1      14.6 74417 3092.0
## - practice_sport:transport_means          2     278.7 74681 3092.1
## - gender:test_prep                        1      36.6 74439 3092.2
## - ethnic_group:is_first_child             4     820.4 75222 3092.4
## - parent_marital_status:transport_means   3     608.0 75010 3092.7
## - gender:is_first_child                   1     113.6 74516 3092.8
## - test_prep:transport_means               1     159.0 74561 3093.2
## - test_prep:practice_sport                2     417.4 74819 3093.2
## - gender:wkly_study_hours                 2     418.8 74821 3093.2
## - test_prep:wkly_study_hours              2     435.0 74837 3093.3
## - is_first_child:transport_means          1     223.9 74626 3093.7
## - gender:practice_sport                   2     478.2 74880 3093.7
## - lunch_type:is_first_child               1     250.2 74652 3093.9
## <none>                                                74402 3093.9
## - lunch_type:transport_means              1     305.0 74707 3094.3
## - parent_educ:practice_sport             10    2677.4 77079 3094.8
## - practice_sport:wkly_study_hours         4    1145.4 75547 3094.9
## - parent_educ:parent_marital_status      14    3963.2 78365 3096.5
## + parent_educ:is_first_child              5     908.9 73493 3096.7
## - ethnic_group:lunch_type                 4    1401.7 75804 3096.9
## - ethnic_group:parent_marital_status     10    2988.4 77390 3097.1
## + practice_sport:is_first_child           2      89.6 74312 3097.2
## + lunch_type:parent_marital_status        3     333.8 74068 3097.2
## - lunch_type:wkly_study_hours             2     987.7 75390 3097.7
## - lunch_type:practice_sport               2    1005.9 75408 3097.8
## + gender:ethnic_group                     4     468.2 73934 3098.2
## - ethnic_group:transport_means            4    1592.6 75995 3098.4
## + gender:parent_marital_status            3     140.4 74262 3098.8
## + parent_educ:transport_means             5     540.0 73862 3099.6
## + parent_marital_status:practice_sport    5     445.6 73956 3100.3
## + gender:parent_educ                      5     357.5 74045 3101.1
## + ethnic_group:practice_sport             8    1093.6 73308 3101.2
## + parent_educ:test_prep                   5     283.3 74119 3101.7
## + parent_educ:lunch_type                  5     216.9 74185 3102.2
## + parent_educ:wkly_study_hours           10    1215.8 73186 3104.2
## + ethnic_group:wkly_study_hours           8     490.9 73911 3106.0
## - parent_marital_status:wkly_study_hours  5    2913.7 77316 3106.6
## - parent_marital_status:is_first_child    2    2779.0 77181 3111.5
## + ethnic_group:parent_educ               20    2651.5 71751 3112.5
## 
## Step:  AIC=3090.82
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:parent_marital_status + test_prep:practice_sport + 
##     test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:parent_marital_status         2     226.9 74745 3088.6
## - ethnic_group:test_prep                  4     755.2 75273 3088.8
## - test_prep:is_first_child                1       3.6 74522 3088.8
## - gender:lunch_type                       1       4.0 74522 3088.8
## - gender:transport_means                  1       5.2 74523 3088.9
## - lunch_type:test_prep                    1      20.2 74538 3089.0
## - transport_means:wkly_study_hours        2     276.9 74795 3089.0
## - practice_sport:transport_means          2     283.8 74802 3089.1
## - gender:test_prep                        1      39.9 74558 3089.1
## - parent_marital_status:transport_means   3     560.5 75079 3089.2
## - gender:is_first_child                   1     131.9 74650 3089.9
## - test_prep:practice_sport                2     389.2 74907 3089.9
## - ethnic_group:is_first_child             4     902.5 75421 3089.9
## - gender:wkly_study_hours                 2     420.9 74939 3090.1
## - test_prep:transport_means               1     178.7 74697 3090.2
## - test_prep:wkly_study_hours              2     447.6 74966 3090.3
## - is_first_child:transport_means          1     207.2 74725 3090.5
## - gender:practice_sport                   2     487.0 75005 3090.7
## <none>                                                74518 3090.8
## - lunch_type:is_first_child               1     281.2 74799 3091.0
## - lunch_type:transport_means              1     316.1 74834 3091.3
## - parent_educ:practice_sport             10    2637.3 77155 3091.3
## - practice_sport:wkly_study_hours         4    1218.6 75737 3092.4
## - ethnic_group:parent_marital_status     10    2949.1 77467 3093.7
## + is_first_child:wkly_study_hours         2     116.1 74402 3093.9
## - ethnic_group:lunch_type                 4    1419.2 75937 3093.9
## + parent_educ:is_first_child              5     851.5 73667 3094.0
## + practice_sport:is_first_child           2      79.9 74438 3094.2
## - parent_educ:parent_marital_status      14    4073.8 78592 3094.2
## + lunch_type:parent_marital_status        3     325.4 74193 3094.2
## - lunch_type:wkly_study_hours             2    1008.5 75527 3094.8
## - ethnic_group:transport_means            4    1571.5 76090 3095.1
## + gender:ethnic_group                     4     463.4 74055 3095.1
## - lunch_type:practice_sport               2    1106.6 75625 3095.5
## + gender:parent_marital_status            3     122.9 74395 3095.8
## + parent_educ:transport_means             5     533.4 73985 3096.6
## + parent_marital_status:practice_sport    5     480.3 74038 3097.0
## + gender:parent_educ                      5     382.2 74136 3097.8
## + ethnic_group:practice_sport             8    1106.0 73412 3098.0
## + parent_educ:test_prep                   5     252.5 74266 3098.8
## + parent_educ:lunch_type                  5     226.9 74291 3099.0
## + parent_educ:wkly_study_hours           10    1196.3 73322 3101.3
## + ethnic_group:wkly_study_hours           8     531.7 73986 3102.6
## - parent_marital_status:wkly_study_hours  5    2935.4 77454 3103.6
## - parent_marital_status:is_first_child    2    2749.1 77267 3108.2
## + ethnic_group:parent_educ               20    2507.0 72011 3110.6
## 
## Step:  AIC=3088.61
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means + transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:is_first_child                1       0.0 74745 3086.6
## - gender:transport_means                  1       3.1 74748 3086.6
## - gender:lunch_type                       1       3.2 74748 3086.6
## - ethnic_group:test_prep                  4     771.7 75517 3086.7
## - lunch_type:test_prep                    1      19.0 74764 3086.8
## - transport_means:wkly_study_hours        2     274.1 75019 3086.8
## - practice_sport:transport_means          2     282.2 75027 3086.8
## - gender:test_prep                        1      33.7 74779 3086.9
## - parent_marital_status:transport_means   3     637.6 75383 3087.6
## - gender:is_first_child                   1     140.0 74885 3087.7
## - gender:wkly_study_hours                 2     427.7 75173 3088.0
## - test_prep:practice_sport                2     430.9 75176 3088.0
## - test_prep:wkly_study_hours              2     443.8 75189 3088.1
## - is_first_child:transport_means          1     194.2 74939 3088.1
## - test_prep:transport_means               1     204.7 74950 3088.2
## - gender:practice_sport                   2     473.1 75218 3088.3
## - ethnic_group:is_first_child             4     989.3 75734 3088.4
## <none>                                                74745 3088.6
## - lunch_type:is_first_child               1     262.7 75008 3088.7
## - parent_educ:practice_sport             10    2614.3 77359 3088.9
## - lunch_type:transport_means              1     313.3 75058 3089.1
## - ethnic_group:parent_marital_status     11    2935.6 77681 3089.3
## - parent_educ:parent_marital_status      15    4085.3 78830 3090.0
## - practice_sport:wkly_study_hours         4    1210.8 75956 3090.1
## + test_prep:parent_marital_status         2     226.9 74518 3090.8
## + is_first_child:wkly_study_hours         2     126.8 74618 3091.6
## + parent_educ:is_first_child              5     831.9 73913 3092.0
## + practice_sport:is_first_child           2      75.7 74669 3092.0
## - ethnic_group:lunch_type                 4    1478.6 76224 3092.2
## + lunch_type:parent_marital_status        3     308.8 74436 3092.2
## - lunch_type:wkly_study_hours             2    1020.1 75765 3092.6
## - lunch_type:practice_sport               2    1054.2 75799 3092.9
## + gender:ethnic_group                     4     446.6 74298 3093.1
## - ethnic_group:transport_means            4    1611.0 76356 3093.2
## + gender:parent_marital_status            3     127.1 74618 3093.6
## + parent_educ:transport_means             5     508.2 74237 3094.6
## + parent_marital_status:practice_sport    5     478.0 74267 3094.8
## + ethnic_group:practice_sport             8    1145.2 73600 3095.5
## + gender:parent_educ                      5     370.5 74374 3095.7
## + parent_educ:lunch_type                  5     254.2 74491 3096.6
## + parent_educ:test_prep                   5     216.4 74529 3096.9
## + parent_educ:wkly_study_hours           10    1231.3 73514 3098.8
## + ethnic_group:wkly_study_hours           8     555.6 74189 3100.2
## - parent_marital_status:wkly_study_hours  6    3151.7 77897 3101.0
## - parent_marital_status:is_first_child    3    2970.8 77716 3105.6
## + ethnic_group:parent_educ               20    2580.0 72165 3107.9
## 
## Step:  AIC=3086.61
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:practice_sport + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:transport_means                  1       3.1 74748 3084.6
## - gender:lunch_type                       1       3.2 74748 3084.6
## - ethnic_group:test_prep                  4     773.4 75518 3084.7
## - lunch_type:test_prep                    1      19.0 74764 3084.8
## - transport_means:wkly_study_hours        2     274.3 75019 3084.8
## - practice_sport:transport_means          2     282.1 75027 3084.8
## - gender:test_prep                        1      33.7 74779 3084.9
## - parent_marital_status:transport_means   3     638.4 75383 3085.6
## - gender:is_first_child                   1     140.6 74886 3085.7
## - gender:wkly_study_hours                 2     429.3 75174 3086.0
## - test_prep:practice_sport                2     431.0 75176 3086.0
## - test_prep:wkly_study_hours              2     443.8 75189 3086.1
## - is_first_child:transport_means          1     194.3 74939 3086.1
## - test_prep:transport_means               1     204.7 74950 3086.2
## - gender:practice_sport                   2     474.3 75219 3086.3
## - ethnic_group:is_first_child             4     990.3 75735 3086.4
## <none>                                                74745 3086.6
## - lunch_type:is_first_child               1     263.8 75009 3086.7
## - parent_educ:practice_sport             10    2614.7 77360 3086.9
## - lunch_type:transport_means              1     315.2 75060 3087.1
## - ethnic_group:parent_marital_status     11    2937.1 77682 3087.3
## - parent_educ:parent_marital_status      15    4085.4 78830 3088.0
## - practice_sport:wkly_study_hours         4    1213.1 75958 3088.1
## + test_prep:is_first_child                1       0.0 74745 3088.6
## + test_prep:parent_marital_status         2     223.3 74522 3088.8
## + is_first_child:wkly_study_hours         2     126.2 74619 3089.6
## + practice_sport:is_first_child           2      75.4 74670 3090.0
## + parent_educ:is_first_child              5     828.7 73916 3090.0
## + lunch_type:parent_marital_status        3     308.7 74436 3090.2
## - ethnic_group:lunch_type                 4    1481.4 76226 3090.2
## - lunch_type:wkly_study_hours             2    1020.8 75766 3090.6
## - lunch_type:practice_sport               2    1055.5 75800 3090.9
## + gender:ethnic_group                     4     446.6 74298 3091.1
## - ethnic_group:transport_means            4    1611.0 76356 3091.2
## + gender:parent_marital_status            3     126.9 74618 3091.6
## + parent_educ:transport_means             5     504.6 74240 3092.6
## + parent_marital_status:practice_sport    5     478.0 74267 3092.8
## + ethnic_group:practice_sport             8    1145.0 73600 3093.5
## + gender:parent_educ                      5     369.4 74376 3093.7
## + parent_educ:lunch_type                  5     254.2 74491 3094.6
## + parent_educ:test_prep                   5     216.1 74529 3094.9
## + parent_educ:wkly_study_hours           10    1230.4 73515 3096.8
## + ethnic_group:wkly_study_hours           8     552.7 74192 3098.2
## - parent_marital_status:wkly_study_hours  6    3152.6 77898 3099.0
## - parent_marital_status:is_first_child    3    2971.0 77716 3103.6
## + ethnic_group:parent_educ               20    2568.1 72177 3106.0
## 
## Step:  AIC=3084.64
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:lunch_type + 
##     gender:test_prep + gender:practice_sport + gender:is_first_child + 
##     gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:lunch_type                       1       3.4 74751 3082.7
## - ethnic_group:test_prep                  4     772.2 75520 3082.7
## - lunch_type:test_prep                    1      19.4 74767 3082.8
## - transport_means:wkly_study_hours        2     274.4 75022 3082.8
## - practice_sport:transport_means          2     282.4 75030 3082.9
## - gender:test_prep                        1      32.1 74780 3082.9
## - parent_marital_status:transport_means   3     637.5 75386 3083.7
## - gender:is_first_child                   1     140.3 74888 3083.7
## - test_prep:practice_sport                2     430.3 75178 3084.0
## - gender:wkly_study_hours                 2     430.5 75179 3084.0
## - test_prep:wkly_study_hours              2     443.4 75191 3084.1
## - is_first_child:transport_means          1     197.9 74946 3084.2
## - test_prep:transport_means               1     209.1 74957 3084.3
## - gender:practice_sport                   2     476.3 75224 3084.4
## - ethnic_group:is_first_child             4     991.8 75740 3084.4
## <none>                                                74748 3084.6
## - lunch_type:is_first_child               1     261.5 75010 3084.7
## - parent_educ:practice_sport             10    2633.2 77381 3085.1
## - lunch_type:transport_means              1     319.1 75067 3085.2
## - ethnic_group:parent_marital_status     11    2959.1 77707 3085.5
## - parent_educ:parent_marital_status      15    4087.6 78836 3086.1
## - practice_sport:wkly_study_hours         4    1210.0 75958 3086.1
## + gender:transport_means                  1       3.1 74745 3086.6
## + test_prep:is_first_child                1       0.0 74748 3086.6
## + test_prep:parent_marital_status         2     221.4 74527 3086.9
## + is_first_child:wkly_study_hours         2     128.0 74620 3087.6
## + practice_sport:is_first_child           2      76.0 74672 3088.0
## + parent_educ:is_first_child              5     823.7 73924 3088.1
## + lunch_type:parent_marital_status        3     311.0 74437 3088.2
## - ethnic_group:lunch_type                 4    1480.1 76228 3088.2
## - lunch_type:wkly_study_hours             2    1018.3 75766 3088.6
## - lunch_type:practice_sport               2    1052.9 75801 3088.9
## + gender:ethnic_group                     4     449.4 74299 3089.1
## - ethnic_group:transport_means            4    1611.1 76359 3089.2
## + gender:parent_marital_status            3     126.5 74622 3089.6
## + parent_educ:transport_means             5     503.5 74245 3090.7
## + parent_marital_status:practice_sport    5     479.0 74269 3090.8
## + ethnic_group:practice_sport             8    1137.2 73611 3091.6
## + gender:parent_educ                      5     368.6 74379 3091.7
## + parent_educ:lunch_type                  5     256.9 74491 3092.6
## + parent_educ:test_prep                   5     215.5 74533 3092.9
## + parent_educ:wkly_study_hours           10    1202.3 73546 3095.1
## + ethnic_group:wkly_study_hours           8     551.9 74196 3096.3
## - parent_marital_status:wkly_study_hours  6    3151.6 77900 3097.0
## - parent_marital_status:is_first_child    3    2984.7 77733 3101.7
## + ethnic_group:parent_educ               20    2567.4 72181 3104.0
## 
## Step:  AIC=3082.66
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:test_prep + gender:practice_sport + 
##     gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:test_prep + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:parent_marital_status + parent_educ:practice_sport + 
##     lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:practice_sport + test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:test_prep                  4     771.6 75523 3080.7
## - transport_means:wkly_study_hours        2     273.4 75025 3080.8
## - lunch_type:test_prep                    1      20.5 74772 3080.8
## - practice_sport:transport_means          2     284.4 75036 3080.9
## - gender:test_prep                        1      31.3 74783 3080.9
## - parent_marital_status:transport_means   3     636.2 75388 3081.7
## - gender:is_first_child                   1     140.5 74892 3081.8
## - gender:wkly_study_hours                 2     428.0 75179 3082.0
## - test_prep:practice_sport                2     433.4 75185 3082.1
## - test_prep:wkly_study_hours              2     443.5 75195 3082.2
## - is_first_child:transport_means          1     195.4 74947 3082.2
## - test_prep:transport_means               1     211.2 74963 3082.3
## - gender:practice_sport                   2     475.6 75227 3082.4
## - ethnic_group:is_first_child             4     989.2 75741 3082.4
## <none>                                                74751 3082.7
## - lunch_type:is_first_child               1     264.5 75016 3082.8
## - parent_educ:practice_sport             10    2629.9 77381 3083.1
## - lunch_type:transport_means              1     323.5 75075 3083.2
## - ethnic_group:parent_marital_status     11    2960.2 77712 3083.6
## - parent_educ:parent_marital_status      15    4086.7 78838 3084.1
## - practice_sport:wkly_study_hours         4    1215.8 75967 3084.2
## + gender:lunch_type                       1       3.4 74748 3084.6
## + gender:transport_means                  1       3.2 74748 3084.6
## + test_prep:is_first_child                1       0.0 74751 3084.7
## + test_prep:parent_marital_status         2     220.7 74531 3084.9
## + is_first_child:wkly_study_hours         2     127.3 74624 3085.7
## + practice_sport:is_first_child           2      74.4 74677 3086.1
## + parent_educ:is_first_child              5     822.7 73929 3086.1
## + lunch_type:parent_marital_status        3     314.3 74437 3086.2
## - ethnic_group:lunch_type                 4    1480.8 76232 3086.2
## - lunch_type:wkly_study_hours             2    1015.8 75767 3086.6
## - lunch_type:practice_sport               2    1077.3 75829 3087.1
## + gender:ethnic_group                     4     446.2 74305 3087.1
## - ethnic_group:transport_means            4    1620.2 76372 3087.3
## + gender:parent_marital_status            3     125.2 74626 3087.7
## + parent_educ:transport_means             5     506.3 74245 3088.7
## + parent_marital_status:practice_sport    5     479.0 74272 3088.9
## + ethnic_group:practice_sport             8    1127.4 73624 3089.7
## + gender:parent_educ                      5     368.0 74383 3089.8
## + parent_educ:lunch_type                  5     259.4 74492 3090.6
## + parent_educ:test_prep                   5     213.8 74538 3091.0
## + parent_educ:wkly_study_hours           10    1201.5 73550 3093.1
## + ethnic_group:wkly_study_hours           8     551.4 74200 3094.3
## - parent_marital_status:wkly_study_hours  6    3192.1 77943 3095.3
## - parent_marital_status:is_first_child    3    2981.5 77733 3099.7
## + ethnic_group:parent_educ               20    2531.3 72220 3102.3
## 
## Step:  AIC=3080.72
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:test_prep + gender:practice_sport + 
##     gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:test_prep                        1      11.2 75534 3078.8
## - transport_means:wkly_study_hours        2     278.8 75802 3078.9
## - lunch_type:test_prep                    1      35.1 75558 3079.0
## - practice_sport:transport_means          2     292.2 75815 3079.0
## - parent_marital_status:transport_means   3     569.2 76092 3079.2
## - gender:is_first_child                   1      97.8 75621 3079.5
## - test_prep:practice_sport                2     392.1 75915 3079.8
## - gender:wkly_study_hours                 2     415.8 75939 3080.0
## - is_first_child:transport_means          1     206.3 75729 3080.3
## - lunch_type:is_first_child               1     230.7 75754 3080.5
## - gender:practice_sport                   2     488.1 76011 3080.5
## - test_prep:transport_means               1     243.1 75766 3080.6
## <none>                                                75523 3080.7
## - ethnic_group:is_first_child             4    1039.2 76562 3080.8
## - ethnic_group:parent_marital_status     11    2923.8 78447 3081.1
## - test_prep:wkly_study_hours              2     590.8 76114 3081.3
## - lunch_type:transport_means              1     353.3 75876 3081.5
## - parent_educ:practice_sport             10    2734.4 78257 3081.7
## - parent_educ:parent_marital_status      15    4073.2 79596 3081.7
## - practice_sport:wkly_study_hours         4    1215.7 76739 3082.1
## + ethnic_group:test_prep                  4     771.6 74751 3082.7
## - ethnic_group:lunch_type                 4    1286.4 76809 3082.7
## + gender:lunch_type                       1       2.7 75520 3082.7
## + gender:transport_means                  1       2.1 75521 3082.7
## + test_prep:is_first_child                1       1.5 75522 3082.7
## + test_prep:parent_marital_status         2     233.9 75289 3082.9
## + is_first_child:wkly_study_hours         2     112.4 75411 3083.8
## + parent_educ:is_first_child              5     859.8 74663 3084.0
## + practice_sport:is_first_child           2      84.3 75439 3084.1
## + lunch_type:parent_marital_status        3     334.5 75188 3084.1
## - lunch_type:wkly_study_hours             2     995.9 76519 3084.4
## - ethnic_group:transport_means            4    1599.8 77123 3085.1
## + gender:parent_marital_status            3     137.8 75385 3085.6
## - lunch_type:practice_sport               2    1217.2 76740 3086.2
## + gender:ethnic_group                     4     290.9 75232 3086.4
## + parent_educ:transport_means             5     542.4 74981 3086.5
## + parent_marital_status:practice_sport    5     462.2 75061 3087.1
## + ethnic_group:practice_sport             8    1117.8 74405 3087.9
## + gender:parent_educ                      5     330.2 75193 3088.1
## + parent_educ:lunch_type                  5     277.0 75246 3088.6
## + parent_educ:test_prep                   5     146.2 75377 3089.6
## + parent_educ:wkly_study_hours           10    1155.0 74368 3091.6
## - parent_marital_status:wkly_study_hours  6    3000.9 78524 3091.7
## + ethnic_group:wkly_study_hours           8     559.8 74963 3092.3
## - parent_marital_status:is_first_child    3    3061.0 78584 3098.2
## + ethnic_group:parent_educ               20    2514.4 73009 3100.7
## 
## Step:  AIC=3078.81
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means + 
##     transport_means:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - transport_means:wkly_study_hours        2     273.8 75808 3076.9
## - practice_sport:transport_means          2     292.1 75826 3077.1
## - lunch_type:test_prep                    1      38.5 75573 3077.1
## - parent_marital_status:transport_means   3     575.3 76109 3077.3
## - gender:is_first_child                   1      93.4 75627 3077.5
## - test_prep:practice_sport                2     389.8 75924 3077.8
## - gender:wkly_study_hours                 2     432.6 75967 3078.2
## - is_first_child:transport_means          1     203.0 75737 3078.4
## - lunch_type:is_first_child               1     227.6 75762 3078.6
## - test_prep:transport_means               1     239.8 75774 3078.7
## - gender:practice_sport                   2     500.9 76035 3078.7
## <none>                                                75534 3078.8
## - ethnic_group:is_first_child             4    1033.7 76568 3078.8
## - test_prep:wkly_study_hours              2     583.8 76118 3079.3
## - ethnic_group:parent_marital_status     11    2952.3 78486 3079.4
## - lunch_type:transport_means              1     358.4 75893 3079.6
## - parent_educ:parent_marital_status      15    4062.5 79597 3079.7
## - parent_educ:practice_sport             10    2755.3 78289 3079.9
## - practice_sport:wkly_study_hours         4    1211.3 76745 3080.2
## + gender:test_prep                        1      11.2 75523 3080.7
## + gender:lunch_type                       1       2.2 75532 3080.8
## - ethnic_group:lunch_type                 4    1289.5 76824 3080.8
## + test_prep:is_first_child                1       1.4 75533 3080.8
## + gender:transport_means                  1       1.2 75533 3080.8
## + ethnic_group:test_prep                  4     751.4 74783 3080.9
## + test_prep:parent_marital_status         2     229.3 75305 3081.0
## + is_first_child:wkly_study_hours         2     113.7 75420 3081.9
## + parent_educ:is_first_child              5     858.1 74676 3082.1
## + practice_sport:is_first_child           2      86.3 75448 3082.1
## + lunch_type:parent_marital_status        3     338.3 75196 3082.2
## - lunch_type:wkly_study_hours             2    1005.4 76540 3082.6
## - ethnic_group:transport_means            4    1607.5 77142 3083.2
## + gender:parent_marital_status            3     142.5 75392 3083.7
## - lunch_type:practice_sport               2    1211.6 76746 3084.2
## + gender:ethnic_group                     4     285.8 75248 3084.6
## + parent_educ:transport_means             5     532.2 75002 3084.6
## + parent_marital_status:practice_sport    5     465.2 75069 3085.2
## + ethnic_group:practice_sport             8    1103.3 74431 3086.1
## + gender:parent_educ                      5     323.0 75211 3086.3
## + parent_educ:lunch_type                  5     280.5 75254 3086.6
## + parent_educ:test_prep                   5     151.5 75383 3087.6
## + parent_educ:wkly_study_hours           10    1155.9 74378 3089.7
## - parent_marital_status:wkly_study_hours  6    2990.8 78525 3089.7
## + ethnic_group:wkly_study_hours           8     568.8 74965 3090.3
## - parent_marital_status:is_first_child    3    3050.1 78584 3096.2
## + ethnic_group:parent_educ               20    2513.7 73020 3098.8
## 
## Step:  AIC=3076.94
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + lunch_type:test_prep + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:test_prep                    1      37.1 75845 3075.2
## - parent_marital_status:transport_means   3     554.6 76363 3075.2
## - practice_sport:transport_means          2     311.7 76120 3075.4
## - gender:is_first_child                   1      96.6 75905 3075.7
## - gender:wkly_study_hours                 2     407.4 76215 3076.1
## - test_prep:practice_sport                2     424.4 76232 3076.2
## - is_first_child:transport_means          1     201.9 76010 3076.5
## - test_prep:transport_means               1     209.2 76017 3076.6
## - lunch_type:is_first_child               1     237.9 76046 3076.8
## - gender:practice_sport                   2     498.4 76306 3076.8
## - ethnic_group:parent_marital_status     11    2879.7 78688 3076.9
## <none>                                                75808 3076.9
## - ethnic_group:is_first_child             4    1044.5 76852 3077.0
## - parent_educ:practice_sport             10    2625.6 78434 3077.0
## - test_prep:wkly_study_hours              2     530.9 76339 3077.1
## - parent_educ:parent_marital_status      15    4007.1 79815 3077.3
## - lunch_type:transport_means              1     332.9 76141 3077.5
## - practice_sport:wkly_study_hours         4    1234.7 77043 3078.5
## + transport_means:wkly_study_hours        2     273.8 75534 3078.8
## + gender:test_prep                        1       6.2 75802 3078.9
## + gender:lunch_type                       1       1.6 75806 3078.9
## + gender:transport_means                  1       1.5 75806 3078.9
## - ethnic_group:lunch_type                 4    1295.3 77103 3078.9
## + test_prep:is_first_child                1       0.3 75808 3078.9
## + ethnic_group:test_prep                  4     760.2 75048 3079.0
## + test_prep:parent_marital_status         2     236.2 75572 3079.1
## + is_first_child:wkly_study_hours         2     128.6 75679 3079.9
## + lunch_type:parent_marital_status        3     366.5 75441 3080.1
## + parent_educ:is_first_child              5     860.6 74947 3080.2
## + practice_sport:is_first_child           2      86.9 75721 3080.3
## - lunch_type:wkly_study_hours             2    1028.6 76837 3080.9
## + gender:parent_marital_status            3     127.2 75681 3081.9
## - ethnic_group:transport_means            4    1734.7 77543 3082.3
## - lunch_type:practice_sport               2    1215.6 77024 3082.3
## + gender:ethnic_group                     4     306.9 75501 3082.6
## + parent_educ:transport_means             5     551.3 75257 3082.6
## + parent_marital_status:practice_sport    5     473.7 75334 3083.2
## + ethnic_group:practice_sport             8    1130.4 74677 3084.1
## + gender:parent_educ                      5     343.9 75464 3084.3
## + parent_educ:lunch_type                  5     307.8 75500 3084.5
## + parent_educ:test_prep                   5     146.0 75662 3085.8
## + parent_educ:wkly_study_hours           10    1197.1 74611 3087.6
## - parent_marital_status:wkly_study_hours  6    3056.3 78864 3088.3
## + ethnic_group:wkly_study_hours           8     470.4 75338 3089.3
## - parent_marital_status:is_first_child    3    2949.0 78757 3093.5
## + ethnic_group:parent_educ               20    2520.2 73288 3097.0
## 
## Step:  AIC=3075.23
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:transport_means + 
##     parent_marital_status:wkly_study_hours + practice_sport:transport_means + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_marital_status:transport_means   3     560.4 76405 3073.6
## - practice_sport:transport_means          2     322.3 76167 3073.7
## - gender:is_first_child                   1     101.3 75946 3074.0
## - gender:wkly_study_hours                 2     403.5 76249 3074.4
## - test_prep:practice_sport                2     429.6 76275 3074.6
## - is_first_child:transport_means          1     190.4 76035 3074.7
## - test_prep:transport_means               1     208.1 76053 3074.8
## - gender:practice_sport                   2     491.6 76337 3075.0
## - ethnic_group:parent_marital_status     11    2862.4 78707 3075.1
## - lunch_type:is_first_child               1     242.6 76088 3075.1
## <none>                                                75845 3075.2
## - test_prep:wkly_study_hours              2     526.9 76372 3075.3
## - ethnic_group:is_first_child             4    1053.8 76899 3075.4
## - parent_educ:practice_sport             10    2648.9 78494 3075.5
## - lunch_type:transport_means              1     311.6 76157 3075.7
## - parent_educ:parent_marital_status      15    4021.2 79866 3075.7
## + lunch_type:test_prep                    1      37.1 75808 3076.9
## - practice_sport:wkly_study_hours         4    1266.5 77111 3077.0
## + transport_means:wkly_study_hours        2     272.4 75573 3077.1
## + gender:test_prep                        1       8.6 75836 3077.2
## + ethnic_group:test_prep                  4     772.6 75072 3077.2
## + gender:lunch_type                       1       2.6 75842 3077.2
## + gender:transport_means                  1       1.9 75843 3077.2
## + test_prep:is_first_child                1       0.4 75845 3077.2
## + test_prep:parent_marital_status         2     236.9 75608 3077.4
## - ethnic_group:lunch_type                 4    1340.5 77186 3077.6
## + is_first_child:wkly_study_hours         2     137.2 75708 3078.2
## + lunch_type:parent_marital_status        3     366.8 75478 3078.4
## + practice_sport:is_first_child           2      91.2 75754 3078.5
## + parent_educ:is_first_child              5     842.0 75003 3078.7
## - lunch_type:wkly_study_hours             2    1005.4 76850 3079.0
## + gender:parent_marital_status            3     121.2 75724 3080.3
## - lunch_type:practice_sport               2    1201.8 77047 3080.5
## - ethnic_group:transport_means            4    1735.4 77580 3080.6
## + gender:ethnic_group                     4     317.8 75527 3080.8
## + parent_educ:transport_means             5     567.5 75278 3080.8
## + parent_marital_status:practice_sport    5     467.7 75377 3081.6
## + ethnic_group:practice_sport             8    1157.3 74688 3082.2
## + gender:parent_educ                      5     355.3 75490 3082.5
## + parent_educ:lunch_type                  5     301.9 75543 3082.9
## + parent_educ:test_prep                   5     144.0 75701 3084.1
## + parent_educ:wkly_study_hours           10    1215.6 74629 3085.7
## - parent_marital_status:wkly_study_hours  6    3086.6 78932 3086.8
## + ethnic_group:wkly_study_hours           8     482.4 75363 3087.5
## - parent_marital_status:is_first_child    3    2971.6 78817 3091.9
## + ethnic_group:parent_educ               20    2528.3 73317 3095.2
## 
## Step:  AIC=3073.57
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours + 
##     practice_sport:transport_means + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - practice_sport:transport_means          2     289.2 76695 3071.8
## - gender:is_first_child                   1     104.0 76509 3072.4
## - parent_educ:parent_marital_status      15    3830.4 80236 3072.4
## - gender:wkly_study_hours                 2     397.3 76803 3072.6
## - test_prep:practice_sport                2     408.6 76814 3072.7
## - ethnic_group:parent_marital_status     11    2815.5 79221 3072.9
## - gender:practice_sport                   2     469.1 76875 3073.2
## - test_prep:transport_means               1     227.5 76633 3073.3
## - lunch_type:is_first_child               1     235.1 76640 3073.4
## - test_prep:wkly_study_hours              2     513.5 76919 3073.5
## <none>                                                76405 3073.6
## - ethnic_group:is_first_child             4    1050.0 77455 3073.6
## - is_first_child:transport_means          1     266.4 76672 3073.6
## - lunch_type:transport_means              1     334.7 76740 3074.2
## - parent_educ:practice_sport             10    2736.7 79142 3074.3
## - practice_sport:wkly_study_hours         4    1246.9 77652 3075.1
## + test_prep:parent_marital_status         2     308.7 76097 3075.2
## + parent_marital_status:transport_means   3     560.4 75845 3075.2
## + lunch_type:test_prep                    1      42.8 76363 3075.2
## + gender:test_prep                        1      14.8 76391 3075.5
## + gender:lunch_type                       1       1.2 76404 3075.6
## + gender:transport_means                  1       1.0 76404 3075.6
## + test_prep:is_first_child                1       0.1 76405 3075.6
## + transport_means:wkly_study_hours        2     249.8 76156 3075.6
## - ethnic_group:lunch_type                 4    1321.6 77727 3075.7
## + ethnic_group:test_prep                  4     702.7 75703 3076.1
## + lunch_type:parent_marital_status        3     361.0 76044 3076.8
## + is_first_child:wkly_study_hours         2      83.7 76322 3076.9
## + practice_sport:is_first_child           2      61.6 76344 3077.1
## - lunch_type:wkly_study_hours             2    1054.0 77459 3077.7
## - ethnic_group:transport_means            4    1591.6 77997 3077.7
## + parent_educ:is_first_child              5     718.4 75687 3078.0
## + gender:parent_marital_status            3     187.7 76218 3078.1
## + gender:ethnic_group                     4     335.7 76070 3079.0
## - lunch_type:practice_sport               2    1274.9 77680 3079.3
## + parent_educ:transport_means             5     466.6 75939 3080.0
## + parent_marital_status:practice_sport    5     458.2 75947 3080.0
## + ethnic_group:practice_sport             8    1209.6 75196 3080.2
## + gender:parent_educ                      5     401.7 76004 3080.5
## + parent_educ:lunch_type                  5     307.1 76098 3081.2
## + parent_educ:test_prep                   5     119.6 76286 3082.7
## - parent_marital_status:wkly_study_hours  6    2935.7 79341 3083.8
## + parent_educ:wkly_study_hours           10    1232.7 75173 3084.0
## + ethnic_group:wkly_study_hours           8     494.3 75911 3085.8
## - parent_marital_status:is_first_child    3    3121.7 79527 3091.2
## + ethnic_group:parent_educ               20    2414.4 73991 3094.6
## 
## Step:  AIC=3071.8
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:parent_marital_status + 
##     parent_educ:practice_sport + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:parent_marital_status      15    3742.3 80437 3069.9
## - ethnic_group:parent_marital_status     11    2688.4 79383 3070.1
## - test_prep:practice_sport                2     378.6 77073 3070.7
## - gender:is_first_child                   1     134.4 76829 3070.8
## - gender:wkly_study_hours                 2     415.0 77109 3071.0
## - gender:practice_sport                   2     415.5 77110 3071.0
## - test_prep:transport_means               1     209.1 76904 3071.4
## - lunch_type:is_first_child               1     249.4 76944 3071.7
## - ethnic_group:is_first_child             4    1038.9 77733 3071.7
## - test_prep:wkly_study_hours              2     514.3 77209 3071.8
## <none>                                                76695 3071.8
## - parent_educ:practice_sport             10    2659.6 79354 3071.9
## - is_first_child:transport_means          1     324.1 77019 3072.3
## - lunch_type:transport_means              1     352.1 77047 3072.5
## - practice_sport:wkly_study_hours         4    1213.3 77908 3073.1
## + test_prep:parent_marital_status         2     318.9 76376 3073.3
## + lunch_type:test_prep                    1      53.6 76641 3073.4
## + practice_sport:transport_means          2     289.2 76405 3073.6
## - ethnic_group:lunch_type                 4    1283.1 77978 3073.6
## + gender:test_prep                        1      15.0 76680 3073.7
## + transport_means:wkly_study_hours        2     270.1 76424 3073.7
## + parent_marital_status:transport_means   3     527.2 76167 3073.7
## + gender:lunch_type                       1       2.2 76692 3073.8
## + gender:transport_means                  1       1.1 76693 3073.8
## + test_prep:is_first_child                1       0.2 76694 3073.8
## + ethnic_group:test_prep                  4     713.2 75981 3074.3
## + lunch_type:parent_marital_status        3     359.8 76335 3075.0
## + is_first_child:wkly_study_hours         2      90.4 76604 3075.1
## + practice_sport:is_first_child           2      60.5 76634 3075.3
## - lunch_type:wkly_study_hours             2    1032.8 77727 3075.7
## - ethnic_group:transport_means            4    1618.0 78313 3076.1
## + parent_educ:is_first_child              5     721.0 75974 3076.2
## + gender:parent_marital_status            3     164.7 76530 3076.5
## + gender:ethnic_group                     4     328.7 76366 3077.3
## - lunch_type:practice_sport               2    1255.8 77950 3077.4
## + parent_marital_status:practice_sport    5     444.6 76250 3078.4
## + ethnic_group:practice_sport             8    1203.1 75491 3078.5
## + parent_educ:transport_means             5     422.0 76273 3078.6
## + gender:parent_educ                      5     396.2 76298 3078.8
## + parent_educ:lunch_type                  5     370.5 76324 3078.9
## + parent_educ:test_prep                   5     141.0 76554 3080.7
## - parent_marital_status:wkly_study_hours  6    2936.1 79631 3082.0
## + parent_educ:wkly_study_hours           10    1143.1 75551 3082.9
## + ethnic_group:wkly_study_hours           8     499.7 76195 3083.9
## - parent_marital_status:is_first_child    3    3103.2 79798 3089.2
## + ethnic_group:parent_educ               20    2362.4 74332 3093.3
## 
## Step:  AIC=3069.91
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:practice_sport + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:practice_sport + 
##     test_prep:transport_means + test_prep:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:practice_sport                2     252.6 80689 3067.8
## - ethnic_group:is_first_child             4     845.9 81283 3068.1
## - gender:wkly_study_hours                 2     337.8 80775 3068.4
## - ethnic_group:lunch_type                 4     964.9 81402 3068.9
## - gender:is_first_child                   1     152.4 80589 3069.0
## - gender:practice_sport                   2     443.1 80880 3069.2
## - test_prep:wkly_study_hours              2     487.4 80924 3069.5
## <none>                                                80437 3069.9
## - is_first_child:transport_means          1     291.8 80729 3070.1
## - ethnic_group:parent_marital_status     11    3119.9 83557 3070.4
## - test_prep:transport_means               1     338.9 80776 3070.4
## - practice_sport:wkly_study_hours         4    1165.6 81602 3070.4
## - lunch_type:is_first_child               1     392.2 80829 3070.8
## - lunch_type:transport_means              1     419.3 80856 3071.0
## - parent_educ:practice_sport             10    2963.0 83400 3071.2
## + lunch_type:test_prep                    1      63.2 80374 3071.4
## + parent_educ:parent_marital_status      15    3742.3 76695 3071.8
## + gender:transport_means                  1      14.0 80423 3071.8
## + gender:lunch_type                       1       1.8 80435 3071.9
## + gender:test_prep                        1       1.5 80435 3071.9
## + test_prep:is_first_child                1       0.2 80437 3071.9
## + transport_means:wkly_study_hours        2     233.9 80203 3072.2
## + practice_sport:transport_means          2     201.1 80236 3072.4
## + is_first_child:wkly_study_hours         2     171.6 80265 3072.7
## + ethnic_group:test_prep                  4     689.7 79747 3072.8
## + parent_marital_status:transport_means   3     369.7 80067 3073.2
## + lunch_type:parent_marital_status        3     335.5 80101 3073.4
## + practice_sport:is_first_child           2      26.1 80411 3073.7
## + test_prep:parent_marital_status         3     293.2 80144 3073.8
## + parent_educ:is_first_child              5     730.0 79707 3074.5
## - ethnic_group:transport_means            4    1749.2 82186 3074.6
## + gender:ethnic_group                     4     429.6 80007 3074.8
## - lunch_type:practice_sport               2    1226.7 81664 3074.8
## + gender:parent_educ                      5     654.3 79783 3075.1
## - lunch_type:wkly_study_hours             2    1303.3 81740 3075.4
## + parent_marital_status:practice_sport    6     872.2 79565 3075.5
## + gender:parent_marital_status            3      19.2 80418 3075.8
## + parent_educ:transport_means             5     433.9 80003 3076.7
## + parent_educ:lunch_type                  5     383.9 80053 3077.1
## + ethnic_group:practice_sport             8    1150.9 79286 3077.4
## - parent_marital_status:wkly_study_hours  6    2787.1 83224 3078.0
## + parent_educ:wkly_study_hours           10    1534.7 78902 3078.6
## + parent_educ:test_prep                   5     161.9 80275 3078.7
## + ethnic_group:wkly_study_hours           8     363.2 80074 3083.2
## - parent_marital_status:is_first_child    3    3025.4 83462 3085.7
## + ethnic_group:parent_educ               20    2639.7 77797 3090.2
## 
## Step:  AIC=3067.76
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type + 
##     ethnic_group:parent_marital_status + ethnic_group:is_first_child + 
##     ethnic_group:transport_means + parent_educ:practice_sport + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:wkly_study_hours                 2     317.4 81007 3066.1
## - ethnic_group:is_first_child             4     876.0 81565 3066.1
## - gender:is_first_child                   1     149.2 80839 3066.8
## - ethnic_group:lunch_type                 4    1028.7 81718 3067.2
## - test_prep:wkly_study_hours              2     478.9 81168 3067.2
## - gender:practice_sport                   2     482.9 81172 3067.3
## <none>                                                80689 3067.8
## - is_first_child:transport_means          1     301.4 80991 3068.0
## - ethnic_group:parent_marital_status     11    3122.9 83812 3068.2
## - test_prep:transport_means               1     362.3 81052 3068.4
## - practice_sport:wkly_study_hours         4    1204.8 81894 3068.5
## - lunch_type:transport_means              1     401.7 81091 3068.7
## - lunch_type:is_first_child               1     414.9 81104 3068.8
## - parent_educ:practice_sport             10    2989.8 83679 3069.2
## + lunch_type:test_prep                    1      68.9 80620 3069.3
## + gender:transport_means                  1      16.0 80673 3069.6
## + gender:lunch_type                       1       3.0 80686 3069.7
## + gender:test_prep                        1       0.9 80689 3069.8
## + test_prep:is_first_child                1       0.5 80689 3069.8
## + test_prep:practice_sport                2     252.6 80437 3069.9
## + transport_means:wkly_study_hours        2     250.9 80439 3069.9
## + practice_sport:transport_means          2     179.0 80510 3070.4
## + parent_educ:parent_marital_status      15    3616.3 77073 3070.7
## + is_first_child:wkly_study_hours         2     142.8 80547 3070.7
## + ethnic_group:test_prep                  4     679.6 80010 3070.8
## + parent_marital_status:transport_means   3     354.1 80335 3071.2
## + lunch_type:parent_marital_status        3     344.3 80345 3071.2
## + test_prep:parent_marital_status         3     342.7 80347 3071.2
## + practice_sport:is_first_child           2      29.2 80660 3071.6
## + parent_educ:is_first_child              5     816.0 79873 3071.8
## - ethnic_group:transport_means            4    1694.6 82384 3072.0
## + gender:parent_educ                      5     703.6 79986 3072.6
## + gender:ethnic_group                     4     422.9 80266 3072.7
## + parent_marital_status:practice_sport    6     896.9 79792 3073.2
## - lunch_type:practice_sport               2    1303.1 81992 3073.2
## + gender:parent_marital_status            3      35.1 80654 3073.5
## - lunch_type:wkly_study_hours             2    1383.7 82073 3073.8
## + parent_educ:transport_means             5     451.8 80238 3074.4
## + parent_educ:lunch_type                  5     429.1 80260 3074.6
## - parent_marital_status:wkly_study_hours  6    2769.9 83459 3075.7
## + ethnic_group:practice_sport             8    1090.2 79599 3075.7
## + parent_educ:wkly_study_hours           10    1608.6 79081 3075.9
## + parent_educ:test_prep                   5     143.5 80546 3076.7
## + ethnic_group:wkly_study_hours           8     358.2 80331 3081.1
## - parent_marital_status:is_first_child    3    3049.0 83738 3083.6
## + ethnic_group:parent_educ               20    2713.0 77976 3087.6
## 
## Step:  AIC=3066.08
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     gender:is_first_child + ethnic_group:lunch_type + ethnic_group:parent_marital_status + 
##     ethnic_group:is_first_child + ethnic_group:transport_means + 
##     parent_educ:practice_sport + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:is_first_child             4     824.9 81832 3064.1
## - gender:is_first_child                   1     157.3 81164 3065.2
## - test_prep:wkly_study_hours              2     469.7 81477 3065.5
## - ethnic_group:lunch_type                 4    1034.1 82041 3065.6
## - gender:practice_sport                   2     527.0 81534 3065.9
## - is_first_child:transport_means          1     270.8 81278 3066.1
## <none>                                                81007 3066.1
## - ethnic_group:parent_marital_status     11    3080.5 84087 3066.1
## - practice_sport:wkly_study_hours         4    1177.4 82184 3066.6
## - test_prep:transport_means               1     371.6 81378 3066.8
## - lunch_type:is_first_child               1     398.6 81405 3067.0
## - lunch_type:transport_means              1     411.4 81418 3067.1
## + lunch_type:test_prep                    1      65.7 80941 3067.6
## + gender:wkly_study_hours                 2     317.4 80689 3067.8
## - parent_educ:practice_sport             10    3056.9 84064 3067.9
## + gender:transport_means                  1      14.9 80992 3068.0
## + gender:test_prep                        1       6.9 81000 3068.0
## + test_prep:is_first_child                1       4.0 81003 3068.1
## + gender:lunch_type                       1       1.5 81005 3068.1
## + test_prep:practice_sport                2     232.2 80775 3068.4
## + transport_means:wkly_study_hours        2     227.6 80779 3068.4
## + practice_sport:transport_means          2     188.6 80818 3068.7
## + is_first_child:wkly_study_hours         2     133.4 80873 3069.1
## + ethnic_group:test_prep                  4     673.4 80333 3069.2
## + test_prep:parent_marital_status         3     361.5 80645 3069.4
## + parent_marital_status:transport_means   3     350.5 80656 3069.5
## + parent_educ:parent_marital_status      15    3542.0 77465 3069.7
## + practice_sport:is_first_child           2      23.4 80983 3069.9
## + lunch_type:parent_marital_status        3     291.6 80715 3069.9
## - ethnic_group:transport_means            4    1664.0 82671 3070.1
## + parent_educ:is_first_child              5     765.7 80241 3070.5
## + gender:ethnic_group                     4     458.3 80549 3070.7
## + gender:parent_educ                      5     716.2 80291 3070.8
## - lunch_type:wkly_study_hours             2    1298.7 82306 3071.5
## + parent_marital_status:practice_sport    6     903.1 80104 3071.5
## - lunch_type:practice_sport               2    1320.2 82327 3071.6
## + gender:parent_marital_status            3      51.8 80955 3071.7
## + parent_educ:transport_means             5     408.3 80598 3073.1
## + parent_educ:wkly_study_hours           10    1753.4 79253 3073.2
## + parent_educ:lunch_type                  5     387.2 80620 3073.2
## + ethnic_group:practice_sport             8    1147.0 79860 3073.7
## + parent_educ:test_prep                   5     166.8 80840 3074.9
## - parent_marital_status:wkly_study_hours  6    3058.9 84066 3075.9
## + ethnic_group:wkly_study_hours           8     326.3 80680 3079.7
## - parent_marital_status:is_first_child    3    2917.4 83924 3080.9
## + ethnic_group:parent_educ               20    2718.5 78288 3085.9
## 
## Step:  AIC=3064.06
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     gender:is_first_child + ethnic_group:lunch_type + ethnic_group:parent_marital_status + 
##     ethnic_group:transport_means + parent_educ:practice_sport + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:lunch_type                 4     852.1 82684 3062.2
## - ethnic_group:parent_marital_status     11    2845.2 84677 3062.2
## - test_prep:wkly_study_hours              2     337.2 82169 3062.5
## - gender:is_first_child                   1      92.9 81925 3062.7
## - is_first_child:transport_means          1     144.4 81976 3063.1
## - gender:practice_sport                   2     513.8 82346 3063.8
## <none>                                                81832 3064.1
## - test_prep:transport_means               1     331.1 82163 3064.4
## - lunch_type:transport_means              1     353.6 82185 3064.6
## - practice_sport:wkly_study_hours         4    1203.5 83035 3064.7
## + lunch_type:test_prep                    1      70.7 81761 3065.6
## - parent_educ:practice_sport             10    3037.2 84869 3065.6
## - lunch_type:is_first_child               1     516.8 82349 3065.8
## + test_prep:is_first_child                1      12.1 81820 3066.0
## + gender:transport_means                  1      11.6 81820 3066.0
## + gender:test_prep                        1       3.5 81828 3066.0
## + gender:lunch_type                       1       1.2 81830 3066.1
## + ethnic_group:is_first_child             4     824.9 81007 3066.1
## + test_prep:practice_sport                2     268.1 81564 3066.1
## + gender:wkly_study_hours                 2     266.2 81565 3066.1
## + transport_means:wkly_study_hours        2     249.9 81582 3066.2
## + is_first_child:wkly_study_hours         2     194.0 81638 3066.7
## + practice_sport:transport_means          2     186.5 81645 3066.7
## + ethnic_group:test_prep                  4     728.6 81103 3066.8
## + test_prep:parent_marital_status         3     433.6 81398 3066.9
## + parent_marital_status:transport_means   3     351.9 81480 3067.5
## + practice_sport:is_first_child           2      25.3 81806 3067.9
## + lunch_type:parent_marital_status        3     240.0 81592 3068.3
## + parent_educ:is_first_child              5     786.2 81046 3068.4
## + gender:ethnic_group                     4     454.0 81378 3068.8
## - lunch_type:wkly_study_hours             2    1224.7 83056 3068.8
## + gender:parent_educ                      5     703.5 81128 3069.0
## + parent_educ:parent_marital_status      15    3382.9 78449 3069.2
## - lunch_type:practice_sport               2    1335.5 83167 3069.6
## + parent_marital_status:practice_sport    6     882.2 80950 3069.7
## - ethnic_group:transport_means            4    1911.7 83743 3069.7
## + gender:parent_marital_status            3      35.0 81797 3069.8
## + parent_educ:wkly_study_hours           10    1830.4 80001 3070.7
## + parent_educ:transport_means             5     445.2 81387 3070.8
## + parent_educ:lunch_type                  5     377.7 81454 3071.3
## + ethnic_group:practice_sport             8    1069.7 80762 3072.3
## + parent_educ:test_prep                   5     160.9 81671 3072.9
## - parent_marital_status:wkly_study_hours  6    2994.3 84826 3073.3
## - parent_marital_status:is_first_child    3    2566.9 84399 3076.3
## + ethnic_group:wkly_study_hours           8     354.1 81478 3077.5
## + ethnic_group:parent_educ               20    2784.5 79047 3083.6
## 
## Step:  AIC=3062.17
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     gender:is_first_child + ethnic_group:parent_marital_status + 
##     ethnic_group:transport_means + parent_educ:practice_sport + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - ethnic_group:parent_marital_status     11   2792.28 85476 3059.8
## - test_prep:wkly_study_hours              2    332.30 83016 3060.5
## - gender:is_first_child                   1     84.77 82769 3060.8
## - is_first_child:transport_means          1    122.86 82807 3061.0
## - gender:practice_sport                   2    436.01 83120 3061.3
## - practice_sport:wkly_study_hours         4   1064.27 83748 3061.7
## <none>                                                82684 3062.2
## - test_prep:transport_means               1    367.25 83051 3062.8
## - lunch_type:transport_means              1    416.94 83101 3063.1
## + lunch_type:test_prep                    1    106.82 82577 3063.4
## - lunch_type:is_first_child               1    457.20 83141 3063.4
## + test_prep:practice_sport                2    327.08 82357 3063.8
## - parent_educ:practice_sport             10   3101.14 85785 3063.9
## + ethnic_group:lunch_type                 4    852.14 81832 3064.1
## + gender:transport_means                  1     14.86 82669 3064.1
## + test_prep:is_first_child                1      5.78 82678 3064.1
## + gender:lunch_type                       1      5.44 82678 3064.1
## + gender:test_prep                        1      4.70 82679 3064.1
## + gender:wkly_study_hours                 2    272.64 82411 3064.2
## + transport_means:wkly_study_hours        2    254.90 82429 3064.3
## + is_first_child:wkly_study_hours         2    193.27 82491 3064.8
## + test_prep:parent_marital_status         3    449.82 82234 3064.9
## + practice_sport:transport_means          2    155.79 82528 3065.1
## + ethnic_group:is_first_child             4    642.90 82041 3065.6
## + parent_marital_status:transport_means   3    349.67 82334 3065.7
## + practice_sport:is_first_child           2     33.45 82650 3065.9
## + ethnic_group:test_prep                  4    566.41 82117 3066.1
## + parent_educ:is_first_child              5    839.05 81845 3066.2
## - lunch_type:wkly_study_hours             2   1133.23 83817 3066.2
## + lunch_type:parent_marital_status        3    269.52 82414 3066.2
## + gender:ethnic_group                     4    456.00 82228 3066.9
## - ethnic_group:transport_means            4   1846.35 84530 3067.2
## + parent_marital_status:practice_sport    6    954.98 81729 3067.3
## + gender:parent_educ                      5    616.92 82067 3067.8
## + gender:parent_marital_status            3     37.83 82646 3067.9
## + parent_educ:transport_means             5    525.02 82159 3068.4
## - lunch_type:practice_sport               2   1543.54 84227 3069.1
## + parent_educ:parent_marital_status      15   3130.53 79553 3069.4
## + ethnic_group:practice_sport             8   1213.72 81470 3069.4
## + parent_educ:lunch_type                  5    340.93 82343 3069.7
## + parent_educ:test_prep                   5    161.91 82522 3071.0
## + parent_educ:wkly_study_hours           10   1527.60 81156 3071.2
## - parent_marital_status:wkly_study_hours  6   3050.50 85734 3071.5
## - parent_marital_status:is_first_child    3   2646.16 85330 3074.8
## + ethnic_group:wkly_study_hours           8    326.65 82357 3075.8
## + ethnic_group:parent_educ               20   2852.94 79831 3081.4
## 
## Step:  AIC=3059.76
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     gender:is_first_child + ethnic_group:transport_means + parent_educ:practice_sport + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:is_first_child                   1      99.6 85576 3058.4
## - practice_sport:wkly_study_hours         4    1008.6 86485 3058.7
## - test_prep:wkly_study_hours              2     479.0 85955 3059.1
## - is_first_child:transport_means          1     198.2 85674 3059.1
## - gender:practice_sport                   2     564.4 86041 3059.7
## <none>                                                85476 3059.8
## - lunch_type:is_first_child               1     308.3 85784 3059.9
## - parent_educ:practice_sport             10    2978.9 88455 3060.0
## - test_prep:transport_means               1     364.2 85840 3060.3
## - lunch_type:transport_means              1     417.7 85894 3060.6
## + test_prep:practice_sport                2     328.5 85148 3061.5
## + lunch_type:test_prep                    1      32.5 85444 3061.5
## + gender:test_prep                        1      14.8 85461 3061.7
## + test_prep:is_first_child                1       1.7 85474 3061.8
## + gender:lunch_type                       1       0.3 85476 3061.8
## + gender:transport_means                  1       0.0 85476 3061.8
## + transport_means:wkly_study_hours        2     244.4 85232 3062.1
## + gender:wkly_study_hours                 2     237.4 85239 3062.1
## + ethnic_group:parent_marital_status     11    2792.3 82684 3062.2
## + ethnic_group:lunch_type                 4     799.3 84677 3062.2
## + practice_sport:transport_means          2     103.1 85373 3063.1
## + parent_marital_status:transport_means   3     372.4 85104 3063.2
## - lunch_type:wkly_study_hours             2    1083.0 86559 3063.2
## + is_first_child:wkly_study_hours         2      80.1 85396 3063.2
## + lunch_type:parent_marital_status        3     364.8 85111 3063.2
## + test_prep:parent_marital_status         3     353.5 85123 3063.3
## + parent_educ:parent_marital_status      15    3706.0 81770 3063.6
## + practice_sport:is_first_child           2      15.9 85460 3063.7
## - ethnic_group:transport_means            4    1765.3 87241 3063.8
## + ethnic_group:test_prep                  4     491.6 84985 3064.4
## + parent_marital_status:practice_sport    6    1039.9 84436 3064.5
## + parent_educ:is_first_child              5     744.1 84732 3064.6
## + gender:parent_marital_status            3     152.7 85323 3064.7
## + ethnic_group:is_first_child             4     412.6 85064 3064.9
## + gender:ethnic_group                     4     376.8 85099 3065.2
## - parent_marital_status:wkly_study_hours  6    2624.6 88101 3065.6
## + parent_educ:transport_means             5     566.9 84909 3065.8
## + parent_educ:wkly_study_hours           10    1851.9 83624 3066.8
## + gender:parent_educ                      5     421.5 85055 3066.8
## + ethnic_group:practice_sport             8    1241.8 84234 3067.1
## - lunch_type:practice_sport               2    1699.0 87175 3067.4
## + parent_educ:lunch_type                  5     306.9 85169 3067.6
## - parent_marital_status:is_first_child    3    2204.5 87681 3068.8
## + parent_educ:test_prep                   5     128.8 85347 3068.9
## + ethnic_group:wkly_study_hours           8     315.5 85161 3073.6
## + ethnic_group:parent_educ               20    2736.0 82740 3080.6
## 
## Step:  AIC=3058.45
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     ethnic_group:transport_means + parent_educ:practice_sport + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:transport_means + 
##     test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours + 
##     is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:wkly_study_hours              2     466.5 86042 3057.7
## - practice_sport:wkly_study_hours         4    1055.8 86632 3057.7
## - is_first_child:transport_means          1     187.3 85763 3057.7
## - lunch_type:is_first_child               1     290.5 85866 3058.4
## <none>                                                85576 3058.4
## - gender:practice_sport                   2     587.3 86163 3058.5
## - test_prep:transport_means               1     362.2 85938 3058.9
## - parent_educ:practice_sport             10    3073.1 88649 3059.3
## - lunch_type:transport_means              1     454.6 86030 3059.6
## + gender:is_first_child                   1      99.6 85476 3059.8
## + lunch_type:test_prep                    1      36.7 85539 3060.2
## + test_prep:practice_sport                2     321.6 85254 3060.2
## + gender:test_prep                        1      10.1 85566 3060.4
## + test_prep:is_first_child                1       3.9 85572 3060.4
## + gender:lunch_type                       1       0.3 85575 3060.4
## + gender:transport_means                  1       0.0 85576 3060.4
## + ethnic_group:parent_marital_status     11    2807.1 82769 3060.8
## + gender:wkly_study_hours                 2     239.8 85336 3060.8
## + transport_means:wkly_study_hours        2     235.6 85340 3060.8
## + ethnic_group:lunch_type                 4     790.3 84785 3061.0
## + practice_sport:transport_means          2     119.8 85456 3061.6
## - lunch_type:wkly_study_hours             2    1069.3 86645 3061.8
## + is_first_child:wkly_study_hours         2      93.1 85483 3061.8
## + parent_marital_status:transport_means   3     378.6 85197 3061.8
## + lunch_type:parent_marital_status        3     373.1 85203 3061.9
## + test_prep:parent_marital_status         3     366.2 85210 3061.9
## + practice_sport:is_first_child           2      17.0 85559 3062.3
## + parent_educ:parent_marital_status      15    3677.7 81898 3062.5
## - ethnic_group:transport_means            4    1832.9 87409 3062.9
## + ethnic_group:test_prep                  4     469.5 85106 3063.2
## + parent_educ:is_first_child              5     746.7 84829 3063.3
## + gender:parent_marital_status            3     164.8 85411 3063.3
## + parent_marital_status:practice_sport    6    1021.0 84555 3063.4
## + gender:ethnic_group                     4     396.7 85179 3063.7
## - parent_marital_status:wkly_study_hours  6    2559.8 88136 3063.8
## + ethnic_group:is_first_child             4     373.2 85203 3063.9
## + parent_educ:transport_means             5     547.7 85028 3064.7
## + parent_educ:wkly_study_hours           10    1883.7 83692 3065.3
## + gender:parent_educ                      5     423.0 85153 3065.5
## + parent_educ:lunch_type                  5     345.4 85230 3066.1
## + ethnic_group:practice_sport             8    1193.1 84383 3066.2
## - lunch_type:practice_sport               2    1747.0 87323 3066.4
## - parent_marital_status:is_first_child    3    2145.8 87722 3067.1
## + parent_educ:test_prep                   5     132.8 85443 3067.5
## + ethnic_group:wkly_study_hours           8     314.1 85262 3072.3
## + ethnic_group:parent_educ               20    2622.3 82953 3080.1
## 
## Step:  AIC=3057.66
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     ethnic_group:transport_means + parent_educ:practice_sport + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:transport_means + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours + 
##     practice_sport:wkly_study_hours + is_first_child:transport_means
## 
##                                          Df Sum of Sq   RSS    AIC
## - is_first_child:transport_means          1     180.8 86223 3056.9
## - practice_sport:wkly_study_hours         4    1089.4 87132 3057.1
## - parent_educ:practice_sport             10    2918.5 88961 3057.3
## - lunch_type:is_first_child               1     245.9 86288 3057.3
## - gender:practice_sport                   2     569.1 86611 3057.6
## <none>                                                86042 3057.7
## - test_prep:transport_means               1     322.8 86365 3057.9
## - lunch_type:transport_means              1     347.8 86390 3058.0
## + test_prep:wkly_study_hours              2     466.5 85576 3058.4
## + ethnic_group:parent_marital_status     11    2953.0 83089 3059.1
## + gender:is_first_child                   1      87.1 85955 3059.1
## + lunch_type:test_prep                    1      28.5 86014 3059.5
## + test_prep:practice_sport                2     315.9 85726 3059.5
## + gender:test_prep                        1       3.7 86039 3059.6
## + test_prep:is_first_child                1       2.4 86040 3059.6
## + gender:lunch_type                       1       0.5 86042 3059.7
## + gender:transport_means                  1       0.1 86042 3059.7
## + gender:wkly_study_hours                 2     231.2 85811 3060.1
## + transport_means:wkly_study_hours        2     203.4 85839 3060.3
## + ethnic_group:lunch_type                 4     765.9 85276 3060.4
## + practice_sport:transport_means          2     121.1 85921 3060.8
## + is_first_child:wkly_study_hours         2      80.3 85962 3061.1
## + parent_marital_status:transport_means   3     367.4 85675 3061.1
## + test_prep:parent_marital_status         3     353.3 85689 3061.2
## + lunch_type:parent_marital_status        3     351.9 85690 3061.2
## - lunch_type:wkly_study_hours             2    1130.2 87172 3061.4
## + practice_sport:is_first_child           2      22.1 86020 3061.5
## - ethnic_group:transport_means            4    1762.4 87805 3061.6
## + ethnic_group:test_prep                  4     563.0 85479 3061.8
## + parent_educ:parent_marital_status      15    3637.1 82405 3062.2
## + parent_educ:is_first_child              5     782.3 85260 3062.3
## + parent_marital_status:practice_sport    6    1062.0 84980 3062.3
## + gender:parent_marital_status            3     132.6 85910 3062.8
## + gender:ethnic_group                     4     414.5 85628 3062.8
## - parent_marital_status:wkly_study_hours  6    2558.9 88601 3062.9
## + parent_educ:wkly_study_hours           10    2045.6 83997 3063.5
## + parent_educ:transport_means             5     565.0 85477 3063.8
## + ethnic_group:is_first_child             4     274.4 85768 3063.8
## + gender:parent_educ                      5     469.8 85572 3064.4
## - lunch_type:practice_sport               2    1596.3 87639 3064.5
## + parent_educ:lunch_type                  5     353.9 85688 3065.2
## + ethnic_group:practice_sport             8    1091.5 84951 3066.1
## - parent_marital_status:is_first_child    3    2170.7 88213 3066.4
## + parent_educ:test_prep                   5     135.1 85907 3066.7
## + ethnic_group:wkly_study_hours           8     351.6 85691 3071.2
## + ethnic_group:parent_educ               20    2649.4 83393 3079.2
## 
## Step:  AIC=3056.9
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     ethnic_group:transport_means + parent_educ:practice_sport + 
##     lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:transport_means + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours + 
##     practice_sport:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - parent_educ:practice_sport             10    2832.5 89055 3056.0
## - practice_sport:wkly_study_hours         4    1063.9 87287 3056.1
## - lunch_type:is_first_child               1     244.7 86468 3056.6
## <none>                                                86223 3056.9
## - gender:practice_sport                   2     601.5 86825 3057.0
## - lunch_type:transport_means              1     345.2 86568 3057.2
## - test_prep:transport_means               1     351.2 86574 3057.3
## + is_first_child:transport_means          1     180.8 86042 3057.7
## + test_prep:wkly_study_hours              2     459.9 85763 3057.7
## + ethnic_group:parent_marital_status     11    3020.0 83203 3057.9
## + gender:is_first_child                   1      77.2 86146 3058.4
## + test_prep:practice_sport                2     317.0 85906 3058.7
## + lunch_type:test_prep                    1      18.6 86204 3058.8
## + test_prep:is_first_child                1       4.4 86219 3058.9
## + gender:test_prep                        1       2.5 86221 3058.9
## + gender:transport_means                  1       1.6 86221 3058.9
## + gender:lunch_type                       1       0.0 86223 3058.9
## + gender:wkly_study_hours                 2     214.7 86008 3059.4
## + transport_means:wkly_study_hours        2     201.8 86021 3059.5
## + ethnic_group:lunch_type                 4     760.6 85462 3059.7
## + practice_sport:transport_means          2     138.2 86085 3059.9
## + parent_marital_status:transport_means   3     425.2 85798 3060.0
## + is_first_child:wkly_study_hours         2      66.5 86156 3060.4
## + test_prep:parent_marital_status         3     354.6 85868 3060.5
## + lunch_type:parent_marital_status        3     348.9 85874 3060.5
## + practice_sport:is_first_child           2      15.4 86208 3060.8
## - ethnic_group:transport_means            4    1773.5 87996 3060.9
## + ethnic_group:test_prep                  4     562.5 85660 3061.0
## - lunch_type:wkly_study_hours             2    1200.3 87423 3061.1
## + parent_educ:is_first_child              5     810.7 85412 3061.3
## + parent_educ:parent_marital_status      15    3644.1 82579 3061.4
## + parent_marital_status:practice_sport    6    1060.8 85162 3061.6
## + gender:ethnic_group                     4     447.2 85776 3061.8
## - parent_marital_status:wkly_study_hours  6    2529.8 88753 3062.0
## + gender:parent_marital_status            3     115.9 86107 3062.1
## + parent_educ:wkly_study_hours           10    2054.9 84168 3062.7
## + parent_educ:transport_means             5     527.1 85696 3063.3
## - lunch_type:practice_sport               2    1567.4 87790 3063.5
## + ethnic_group:is_first_child             4     198.1 86025 3063.5
## + gender:parent_educ                      5     456.3 85767 3063.8
## + parent_educ:lunch_type                  5     338.7 85884 3064.6
## + ethnic_group:practice_sport             8    1146.4 85077 3065.0
## - parent_marital_status:is_first_child    3    2120.8 88344 3065.2
## + parent_educ:test_prep                   5     168.1 86055 3065.7
## + ethnic_group:wkly_study_hours           8     368.5 85854 3070.4
## + ethnic_group:parent_educ               20    2575.7 83647 3079.0
## 
## Step:  AIC=3055.97
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     ethnic_group:transport_means + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:transport_means + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours + 
##     practice_sport:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - practice_sport:wkly_study_hours         4     914.5 89970 3054.0
## - gender:practice_sport                   2     409.2 89465 3054.7
## - lunch_type:is_first_child               1     155.2 89211 3055.0
## <none>                                                89055 3056.0
## - lunch_type:transport_means              1     306.2 89362 3056.0
## - test_prep:transport_means               1     380.6 89436 3056.5
## + gender:is_first_child                   1     165.2 88890 3056.9
## + parent_educ:practice_sport             10    2832.5 86223 3056.9
## + is_first_child:transport_means          1      94.7 88961 3057.3
## + lunch_type:test_prep                    1      36.5 89019 3057.7
## + gender:test_prep                        1      19.6 89036 3057.8
## + gender:transport_means                  1      16.0 89039 3057.9
## + test_prep:wkly_study_hours              2     307.5 88748 3057.9
## + gender:lunch_type                       1       5.0 89050 3057.9
## + test_prep:is_first_child                1       2.3 89053 3057.9
## + gender:wkly_study_hours                 2     281.6 88774 3058.1
## + test_prep:practice_sport                2     274.1 88781 3058.2
## + parent_marital_status:transport_means   3     536.1 88519 3058.4
## + parent_educ:is_first_child              5    1120.5 87935 3058.5
## + ethnic_group:parent_marital_status     11    2866.7 86189 3058.7
## + parent_educ:parent_marital_status      15    4025.6 85030 3058.7
## + practice_sport:transport_means          2     128.4 88927 3059.1
## + ethnic_group:lunch_type                 4     727.7 88328 3059.1
## + transport_means:wkly_study_hours        2      91.2 88964 3059.4
## + test_prep:parent_marital_status         3     363.7 88692 3059.6
## + is_first_child:wkly_study_hours         2      59.9 88996 3059.6
## - parent_marital_status:wkly_study_hours  6    2422.9 91478 3059.8
## - lunch_type:wkly_study_hours             2    1192.1 90248 3059.8
## + ethnic_group:test_prep                  4     620.7 88435 3059.8
## + practice_sport:is_first_child           2      13.6 89042 3059.9
## + lunch_type:parent_marital_status        3     260.3 88795 3060.2
## - ethnic_group:transport_means            4    1888.2 90944 3060.3
## - lunch_type:practice_sport               2    1306.9 90362 3060.6
## + gender:ethnic_group                     4     493.9 88561 3060.7
## + gender:parent_marital_status            3     188.4 88867 3060.7
## + parent_educ:wkly_study_hours           10    2257.7 86798 3060.8
## + parent_marital_status:practice_sport    6     871.7 88184 3062.2
## + ethnic_group:is_first_child             4     259.4 88796 3062.2
## + parent_educ:transport_means             5     535.3 88520 3062.4
## + ethnic_group:practice_sport             8    1361.2 87694 3062.9
## + gender:parent_educ                      5     452.5 88603 3063.0
## - parent_marital_status:is_first_child    3    2116.2 91172 3063.8
## + parent_educ:lunch_type                  5     311.0 88744 3063.9
## + parent_educ:test_prep                   5     246.7 88809 3064.3
## + ethnic_group:wkly_study_hours           8     414.2 88641 3069.2
## + ethnic_group:parent_educ               20    2184.6 86871 3081.3
## - parent_educ                             5    6212.6 95268 3085.8
## 
## Step:  AIC=3053.99
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     ethnic_group:transport_means + lunch_type:practice_sport + 
##     lunch_type:is_first_child + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:transport_means + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:is_first_child               1     104.8 90075 3052.7
## - gender:practice_sport                   2     480.0 90450 3053.1
## - lunch_type:transport_means              1     253.2 90223 3053.7
## <none>                                                89970 3054.0
## - test_prep:transport_means               1     362.9 90333 3054.4
## + gender:is_first_child                   1     220.7 89749 3054.5
## + is_first_child:transport_means          1      78.8 89891 3055.5
## + lunch_type:test_prep                    1      55.0 89915 3055.6
## + test_prep:wkly_study_hours              2     329.5 89640 3055.8
## + gender:test_prep                        1      17.9 89952 3055.9
## + test_prep:is_first_child                1       8.8 89961 3055.9
## + gender:transport_means                  1       6.2 89964 3055.9
## + practice_sport:wkly_study_hours         4     914.5 89055 3056.0
## + gender:lunch_type                       1       3.0 89967 3056.0
## + test_prep:practice_sport                2     288.9 89681 3056.1
## + parent_educ:practice_sport             10    2683.0 87287 3056.1
## + gender:wkly_study_hours                 2     260.5 89709 3056.3
## + parent_marital_status:transport_means   3     536.5 89433 3056.5
## - ethnic_group:transport_means            4    1731.1 91701 3057.2
## + transport_means:wkly_study_hours        2     106.2 89864 3057.3
## + practice_sport:transport_means          2     105.7 89864 3057.3
## + is_first_child:wkly_study_hours         2     105.5 89864 3057.3
## - lunch_type:wkly_study_hours             2    1121.3 91091 3057.3
## + parent_educ:parent_marital_status      15    3959.8 86010 3057.4
## + parent_educ:is_first_child              5     962.3 89008 3057.7
## + ethnic_group:parent_marital_status     11    2751.1 87219 3057.7
## + test_prep:parent_marital_status         3     339.8 89630 3057.8
## + ethnic_group:test_prep                  4     625.2 89345 3057.9
## + practice_sport:is_first_child           2      16.4 89954 3057.9
## + ethnic_group:lunch_type                 4     613.6 89356 3058.0
## - lunch_type:practice_sport               2    1223.0 91193 3058.0
## + gender:ethnic_group                     4     541.3 89429 3058.4
## - parent_marital_status:wkly_study_hours  6    2566.6 92537 3058.6
## + gender:parent_marital_status            3     213.7 89756 3058.6
## + lunch_type:parent_marital_status        3     185.9 89784 3058.8
## + parent_educ:wkly_study_hours           10    2163.2 87807 3059.6
## + ethnic_group:is_first_child             4     308.4 89662 3060.0
## + parent_educ:transport_means             5     606.4 89364 3060.0
## + parent_marital_status:practice_sport    6     804.4 89166 3060.7
## + gender:parent_educ                      5     467.2 89503 3060.9
## + ethnic_group:practice_sport             8    1351.5 88618 3061.1
## - parent_marital_status:is_first_child    3    2027.1 91997 3061.1
## + parent_educ:lunch_type                  5     369.3 89601 3061.6
## + parent_educ:test_prep                   5     264.7 89705 3062.3
## + ethnic_group:wkly_study_hours           8     442.1 89528 3067.1
## + ethnic_group:parent_educ               20    2078.3 87892 3080.2
## - parent_educ                             5    6298.3 96268 3083.9
## 
## Step:  AIC=3052.68
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + gender:practice_sport + 
##     ethnic_group:transport_means + lunch_type:practice_sport + 
##     lunch_type:transport_means + lunch_type:wkly_study_hours + 
##     test_prep:transport_means + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - gender:practice_sport                   2     526.0 90601 3052.1
## - lunch_type:transport_means              1     243.3 90318 3052.3
## <none>                                                90075 3052.7
## - test_prep:transport_means               1     340.3 90415 3052.9
## + gender:is_first_child                   1     202.2 89873 3053.3
## + lunch_type:is_first_child               1     104.8 89970 3054.0
## + is_first_child:transport_means          1      77.3 89997 3054.2
## + lunch_type:test_prep                    1      62.2 90012 3054.3
## + gender:test_prep                        1      14.6 90060 3054.6
## + test_prep:is_first_child                1      11.9 90063 3054.6
## + gender:transport_means                  1       3.2 90072 3054.7
## + gender:lunch_type                       1       2.1 90073 3054.7
## + test_prep:wkly_study_hours              2     305.6 89769 3054.7
## + test_prep:practice_sport                2     299.1 89776 3054.7
## + practice_sport:wkly_study_hours         4     864.0 89211 3055.0
## + gender:wkly_study_hours                 2     256.1 89819 3055.0
## + parent_marital_status:transport_means   3     532.3 89542 3055.2
## + parent_educ:practice_sport             10    2607.2 87468 3055.3
## + parent_educ:parent_marital_status      15    4009.3 86065 3055.8
## + is_first_child:wkly_study_hours         2     126.1 89949 3055.8
## - ethnic_group:transport_means            4    1728.8 91804 3055.9
## + transport_means:wkly_study_hours        2     113.9 89961 3055.9
## + practice_sport:transport_means          2     112.5 89962 3055.9
## - lunch_type:wkly_study_hours             2    1152.6 91227 3056.2
## + test_prep:parent_marital_status         3     350.7 89724 3056.4
## + parent_educ:is_first_child              5     948.3 89126 3056.4
## - lunch_type:practice_sport               2    1201.6 91276 3056.5
## + practice_sport:is_first_child           2      20.0 90055 3056.6
## + ethnic_group:lunch_type                 4     607.8 89467 3056.7
## + ethnic_group:test_prep                  4     594.8 89480 3056.8
## + gender:ethnic_group                     4     554.4 89520 3057.0
## + ethnic_group:parent_marital_status     11    2638.8 87436 3057.1
## + gender:parent_marital_status            3     203.9 89871 3057.3
## + lunch_type:parent_marital_status        3     174.4 89900 3057.5
## - parent_marital_status:wkly_study_hours  6    2636.8 92712 3057.7
## + ethnic_group:is_first_child             4     345.1 89730 3058.4
## + parent_educ:wkly_study_hours           10    2142.9 87932 3058.5
## + parent_educ:transport_means             5     600.4 89474 3058.7
## + gender:parent_educ                      5     465.6 89609 3059.6
## + ethnic_group:practice_sport             8    1357.1 88718 3059.7
## + parent_marital_status:practice_sport    6     716.6 89358 3060.0
## - parent_marital_status:is_first_child    3    2113.0 92188 3060.4
## + parent_educ:lunch_type                  5     343.3 89731 3060.4
## + parent_educ:test_prep                   5     264.1 89811 3060.9
## + ethnic_group:wkly_study_hours           8     452.4 89622 3065.7
## + ethnic_group:parent_educ               20    2115.9 87959 3078.7
## - parent_educ                             5    6269.5 96344 3082.4
## 
## Step:  AIC=3052.12
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     lunch_type:practice_sport + lunch_type:transport_means + 
##     lunch_type:wkly_study_hours + test_prep:transport_means + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - lunch_type:transport_means              1     262.4 90863 3051.8
## <none>                                                90601 3052.1
## - test_prep:transport_means               1     326.9 90928 3052.2
## + gender:practice_sport                   2     526.0 90075 3052.7
## + gender:is_first_child                   1     218.3 90382 3052.7
## + lunch_type:is_first_child               1     150.8 90450 3053.1
## + is_first_child:transport_means          1      90.8 90510 3053.5
## + lunch_type:test_prep                    1      63.7 90537 3053.7
## + gender:test_prep                        1      21.3 90579 3054.0
## + test_prep:practice_sport                2     327.6 90273 3054.0
## + practice_sport:wkly_study_hours         4     930.4 89670 3054.0
## + gender:transport_means                  1       8.0 90593 3054.1
## + test_prep:is_first_child                1       7.2 90594 3054.1
## + gender:lunch_type                       1       2.4 90598 3054.1
## + test_prep:wkly_study_hours              2     303.1 90298 3054.1
## + gender:wkly_study_hours                 2     298.6 90302 3054.2
## + parent_marital_status:transport_means   3     501.6 90099 3054.8
## + parent_educ:parent_marital_status      15    4059.5 86541 3055.1
## + transport_means:wkly_study_hours        2     140.5 90460 3055.2
## + is_first_child:wkly_study_hours         2     130.1 90471 3055.3
## - ethnic_group:transport_means            4    1762.1 92363 3055.5
## + practice_sport:transport_means          2      85.4 90515 3055.6
## - lunch_type:wkly_study_hours             2    1156.5 91757 3055.6
## + parent_educ:is_first_child              5     955.4 89645 3055.9
## + ethnic_group:parent_marital_status     11    2757.1 87844 3055.9
## + test_prep:parent_marital_status         3     340.6 90260 3055.9
## + practice_sport:is_first_child           2      14.2 90587 3056.0
## - lunch_type:practice_sport               2    1234.5 91835 3056.1
## + ethnic_group:test_prep                  4     608.3 89992 3056.1
## + parent_educ:practice_sport             10    2370.5 88230 3056.5
## + ethnic_group:lunch_type                 4     550.1 90051 3056.5
## - parent_marital_status:wkly_study_hours  6    2560.9 93162 3056.6
## + gender:ethnic_group                     4     526.6 90074 3056.7
## + gender:parent_marital_status            3     213.9 90387 3056.7
## + lunch_type:parent_marital_status        3     164.7 90436 3057.0
## + ethnic_group:is_first_child             4     357.4 90243 3057.8
## + parent_educ:transport_means             5     589.9 90011 3058.3
## + ethnic_group:practice_sport             8    1489.7 89111 3058.3
## + parent_educ:wkly_study_hours           10    2057.4 88543 3058.6
## + gender:parent_educ                      5     482.3 90118 3059.0
## - parent_marital_status:is_first_child    3    2053.4 92654 3059.3
## + parent_marital_status:practice_sport    6     723.2 89878 3059.4
## + parent_educ:lunch_type                  5     389.3 90212 3059.6
## + parent_educ:test_prep                   5     259.3 90341 3060.4
## + ethnic_group:wkly_study_hours           8     436.2 90165 3065.3
## + ethnic_group:parent_educ               20    2189.7 88411 3077.7
## - parent_educ                             5    6278.7 96879 3081.7
## - gender                                  1    8889.6 99490 3105.3
## 
## Step:  AIC=3051.82
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     lunch_type:practice_sport + lunch_type:wkly_study_hours + 
##     test_prep:transport_means + parent_marital_status:is_first_child + 
##     parent_marital_status:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## - test_prep:transport_means               1     300.1 91163 3051.8
## <none>                                                90863 3051.8
## + lunch_type:transport_means              1     262.4 90601 3052.1
## + gender:is_first_child                   1     254.3 90609 3052.2
## + gender:practice_sport                   2     545.1 90318 3052.3
## + lunch_type:is_first_child               1     138.9 90724 3052.9
## + is_first_child:transport_means          1      89.3 90774 3053.2
## + lunch_type:test_prep                    1      40.2 90823 3053.6
## + gender:test_prep                        1      27.3 90836 3053.6
## + test_prep:is_first_child                1      16.5 90847 3053.7
## + gender:transport_means                  1      13.3 90850 3053.7
## + test_prep:practice_sport                2     311.6 90551 3053.8
## + gender:lunch_type                       1       0.7 90862 3053.8
## + gender:wkly_study_hours                 2     303.7 90559 3053.8
## + practice_sport:wkly_study_hours         4     876.1 89987 3054.1
## + test_prep:wkly_study_hours              2     231.4 90632 3054.3
## + parent_marital_status:transport_means   3     501.6 90362 3054.6
## + parent_educ:parent_marital_status      15    4074.5 86789 3054.8
## + transport_means:wkly_study_hours        2     135.8 90727 3054.9
## + is_first_child:wkly_study_hours         2     130.2 90733 3055.0
## - ethnic_group:transport_means            4    1751.0 92614 3055.1
## - lunch_type:wkly_study_hours             2    1125.4 91989 3055.1
## + practice_sport:transport_means          2      93.8 90769 3055.2
## - lunch_type:practice_sport               2    1176.8 92040 3055.4
## + test_prep:parent_marital_status         3     352.3 90511 3055.5
## + ethnic_group:parent_marital_status     11    2754.8 88108 3055.7
## + practice_sport:is_first_child           2      18.0 90845 3055.7
## + parent_educ:is_first_child              5     919.1 89944 3055.8
## + ethnic_group:test_prep                  4     595.6 90267 3055.9
## + ethnic_group:lunch_type                 4     591.5 90272 3056.0
## + gender:parent_marital_status            3     236.6 90627 3056.3
## - parent_marital_status:wkly_study_hours  6    2586.1 93449 3056.4
## + parent_educ:practice_sport             10    2339.6 88524 3056.4
## + gender:ethnic_group                     4     509.1 90354 3056.5
## + lunch_type:parent_marital_status        3     183.6 90680 3056.6
## + ethnic_group:is_first_child             4     324.0 90539 3057.7
## + parent_educ:transport_means             5     598.1 90265 3057.9
## + gender:parent_educ                      5     547.4 90316 3058.3
## + parent_educ:wkly_study_hours           10    2035.7 88827 3058.4
## + ethnic_group:practice_sport             8    1397.2 89466 3058.7
## + parent_marital_status:practice_sport    6     746.8 90116 3058.9
## - parent_marital_status:is_first_child    3    2062.9 92926 3059.1
## + parent_educ:lunch_type                  5     398.6 90465 3059.2
## + parent_educ:test_prep                   5     285.8 90577 3060.0
## + ethnic_group:wkly_study_hours           8     399.8 90463 3065.2
## + ethnic_group:parent_educ               20    2151.2 88712 3077.7
## - parent_educ                             5    6148.1 97011 3080.4
## - gender                                  1    8826.3 99689 3104.5
## 
## Step:  AIC=3051.77
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type + 
##     test_prep + parent_marital_status + practice_sport + is_first_child + 
##     transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     lunch_type:practice_sport + lunch_type:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours
## 
##                                          Df Sum of Sq   RSS    AIC
## <none>                                                91163 3051.8
## + test_prep:transport_means               1     300.1 90863 3051.8
## + gender:is_first_child                   1     257.6 90906 3052.1
## + lunch_type:transport_means              1     235.6 90928 3052.2
## + gender:practice_sport                   2     530.8 90632 3052.3
## + lunch_type:is_first_child               1     114.5 91049 3053.0
## + is_first_child:transport_means          1     108.6 91055 3053.1
## + lunch_type:test_prep                    1      42.2 91121 3053.5
## + gender:transport_means                  1      24.2 91139 3053.6
## + gender:test_prep                        1      23.3 91140 3053.6
## + test_prep:is_first_child                1      18.2 91145 3053.7
## + test_prep:practice_sport                2     325.8 90837 3053.7
## + gender:wkly_study_hours                 2     322.6 90841 3053.7
## + gender:lunch_type                       1       0.0 91163 3053.8
## + practice_sport:wkly_study_hours         4     872.4 90291 3054.1
## + parent_educ:parent_marital_status      15    4174.7 86989 3054.1
## - lunch_type:wkly_study_hours             2     997.2 92160 3054.2
## + parent_marital_status:transport_means   3     537.0 90626 3054.3
## + test_prep:wkly_study_hours              2     211.0 90952 3054.4
## + is_first_child:wkly_study_hours         2     140.3 91023 3054.9
## + transport_means:wkly_study_hours        2     101.6 91062 3055.1
## + practice_sport:transport_means          2      92.2 91071 3055.2
## + test_prep:parent_marital_status         3     391.9 90771 3055.2
## - lunch_type:practice_sport               2    1208.9 92372 3055.5
## + parent_educ:is_first_child              5     948.5 90215 3055.6
## + ethnic_group:parent_marital_status     11    2759.5 88404 3055.6
## + practice_sport:is_first_child           2      16.4 91147 3055.7
## + ethnic_group:lunch_type                 4     617.0 90546 3055.8
## - ethnic_group:transport_means            4    1874.3 93037 3055.8
## - parent_marital_status:wkly_study_hours  6    2516.2 93679 3055.8
## + ethnic_group:test_prep                  4     578.0 90585 3056.0
## + gender:parent_marital_status            3     248.6 90915 3056.2
## + parent_educ:practice_sport             10    2364.5 88799 3056.3
## + gender:ethnic_group                     4     528.5 90635 3056.3
## + lunch_type:parent_marital_status        3     187.1 90976 3056.6
## + ethnic_group:is_first_child             4     297.7 90866 3057.8
## + parent_educ:transport_means             5     601.1 90562 3057.9
## + gender:parent_educ                      5     541.0 90622 3058.3
## + ethnic_group:practice_sport             8    1451.3 89712 3058.3
## + parent_educ:wkly_study_hours           10    2050.0 89113 3058.3
## + parent_marital_status:practice_sport    6     769.8 90393 3058.8
## + parent_educ:lunch_type                  5     420.7 90743 3059.0
## - parent_marital_status:is_first_child    3    2087.3 93251 3059.1
## + parent_educ:test_prep                   5     312.8 90850 3059.7
## + ethnic_group:wkly_study_hours           8     406.7 90757 3065.1
## + ethnic_group:parent_educ               20    2088.9 89074 3078.1
## - test_prep                               1    4865.5 96029 3080.4
## - parent_educ                             5    6366.3 97530 3081.6
## - gender                                  1    8627.7 99791 3103.1
summary(stepwise_model_read)
## 
## Call:
## lm(formula = reading_score ~ gender + ethnic_group + parent_educ + 
##     lunch_type + test_prep + parent_marital_status + practice_sport + 
##     is_first_child + transport_means + wkly_study_hours + ethnic_group:transport_means + 
##     lunch_type:practice_sport + lunch_type:wkly_study_hours + 
##     parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours, 
##     data = df_4_mdl_read)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -44.540  -8.273  -0.267   9.481  33.728 
## 
## Coefficients:
##                                                     Estimate Std. Error t value
## (Intercept)                                          64.0126     5.6402  11.349
## gendermale                                           -7.9731     1.1041  -7.221
## ethnic_groupgroup B                                   4.0052     3.7361   1.072
## ethnic_groupgroup C                                   4.5817     3.4195   1.340
## ethnic_groupgroup D                                   4.6170     3.5000   1.319
## ethnic_groupgroup E                                  13.9574     3.8663   3.610
## parent_educbachelor's degree                          3.3736     1.9408   1.738
## parent_educhigh school                               -5.9247     1.6817  -3.523
## parent_educmaster's degree                            3.4397     2.4234   1.419
## parent_educsome college                              -2.3224     1.6870  -1.377
## parent_educsome high school                          -5.3232     1.6969  -3.137
## lunch_typestandard                                    2.0599     3.8020   0.542
## test_prepnone                                        -6.2162     1.1463  -5.423
## parent_marital_statusmarried                         10.2557     4.0650   2.523
## parent_marital_statussingle                          -0.8882     4.4420  -0.200
## parent_marital_statuswidowed                         17.2457    10.8292   1.593
## practice_sportregularly                              -4.4245     3.2294  -1.370
## practice_sportsometimes                              -5.4217     3.1279  -1.733
## is_first_childyes                                     8.8087     3.3685   2.615
## transport_meansschool_bus                             7.1540     3.8499   1.858
## wkly_study_hours> 10                                -15.1280     5.0552  -2.993
## wkly_study_hours10-May                                1.2358     3.6575   0.338
## ethnic_groupgroup B:transport_meansschool_bus        -8.5078     4.6456  -1.831
## ethnic_groupgroup C:transport_meansschool_bus        -8.7787     4.3480  -2.019
## ethnic_groupgroup D:transport_meansschool_bus        -2.4914     4.4269  -0.563
## ethnic_groupgroup E:transport_meansschool_bus       -12.1513     4.8881  -2.486
## lunch_typestandard:practice_sportregularly            4.3134     3.9100   1.103
## lunch_typestandard:practice_sportsometimes            9.0693     3.8110   2.380
## lunch_typestandard:wkly_study_hours> 10               6.1827     3.4568   1.789
## lunch_typestandard:wkly_study_hours10-May            -1.3341     2.6912  -0.496
## parent_marital_statusmarried:is_first_childyes      -10.3012     3.6911  -2.791
## parent_marital_statussingle:is_first_childyes        -2.7153     4.1037  -0.662
## parent_marital_statuswidowed:is_first_childyes      -11.5351     8.6888  -1.328
## parent_marital_statusmarried:wkly_study_hours> 10    11.8333     4.9161   2.407
## parent_marital_statussingle:wkly_study_hours> 10     20.4572     5.5006   3.719
## parent_marital_statuswidowed:wkly_study_hours> 10     5.7848    14.3577   0.403
## parent_marital_statusmarried:wkly_study_hours10-May   1.7018     3.6640   0.464
## parent_marital_statussingle:wkly_study_hours10-May    5.0455     4.1368   1.220
## parent_marital_statuswidowed:wkly_study_hours10-May  -3.6043    10.7836  -0.334
##                                                     Pr(>|t|)    
## (Intercept)                                          < 2e-16 ***
## gendermale                                          1.72e-12 ***
## ethnic_groupgroup B                                 0.284174    
## ethnic_groupgroup C                                 0.180841    
## ethnic_groupgroup D                                 0.187673    
## ethnic_groupgroup E                                 0.000334 ***
## parent_educbachelor's degree                        0.082717 .  
## parent_educhigh school                              0.000462 ***
## parent_educmaster's degree                          0.156352    
## parent_educsome college                             0.169188    
## parent_educsome high school                         0.001798 ** 
## lunch_typestandard                                  0.588175    
## test_prepnone                                       8.79e-08 ***
## parent_marital_statusmarried                        0.011918 *  
## parent_marital_statussingle                         0.841585    
## parent_marital_statuswidowed                        0.111840    
## practice_sportregularly                             0.171222    
## practice_sportsometimes                             0.083598 .  
## is_first_childyes                                   0.009167 ** 
## transport_meansschool_bus                           0.063672 .  
## wkly_study_hours> 10                                0.002890 ** 
## wkly_study_hours10-May                              0.735589    
## ethnic_groupgroup B:transport_meansschool_bus       0.067585 .  
## ethnic_groupgroup C:transport_meansschool_bus       0.043967 *  
## ethnic_groupgroup D:transport_meansschool_bus       0.573809    
## ethnic_groupgroup E:transport_meansschool_bus       0.013218 *  
## lunch_typestandard:practice_sportregularly          0.270437    
## lunch_typestandard:practice_sportsometimes          0.017661 *  
## lunch_typestandard:wkly_study_hours> 10             0.074233 .  
## lunch_typestandard:wkly_study_hours10-May           0.620296    
## parent_marital_statusmarried:is_first_childyes      0.005440 ** 
## parent_marital_statussingle:is_first_childyes       0.508448    
## parent_marital_statuswidowed:is_first_childyes      0.184867    
## parent_marital_statusmarried:wkly_study_hours> 10   0.016410 *  
## parent_marital_statussingle:wkly_study_hours> 10    0.000220 ***
## parent_marital_statuswidowed:wkly_study_hours> 10   0.687173    
## parent_marital_statusmarried:wkly_study_hours10-May 0.642503    
## parent_marital_statussingle:wkly_study_hours10-May  0.223116    
## parent_marital_statuswidowed:wkly_study_hours10-May 0.738324    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 12.86 on 551 degrees of freedom
## Multiple R-squared:  0.3254, Adjusted R-squared:  0.2789 
## F-statistic: 6.995 on 38 and 551 DF,  p-value: < 2.2e-16

Diagnostics

Writing

plot(stepwise_model_write)

step_as_lm_write=lm(formula = writing_score ~ gender + ethnic_group + parent_educ + 
    lunch_type + test_prep + parent_marital_status + practice_sport + 
    is_first_child + transport_means + wkly_study_hours + ethnic_group:transport_means + 
    lunch_type:practice_sport + lunch_type:wkly_study_hours + 
    parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours, data = df_4_mdl_write)

library('MASS')
## 
## Attaching package: 'MASS'
## The following object is masked from 'package:gtsummary':
## 
##     select
## The following object is masked from 'package:dplyr':
## 
##     select
boxcox(step_as_lm_write)

step_as_lm_write=lm(formula = (writing_score)^2 ~ gender + ethnic_group + parent_educ + 
    lunch_type + test_prep + parent_marital_status + practice_sport + 
    is_first_child + transport_means + wkly_study_hours + ethnic_group:transport_means + 
    lunch_type:practice_sport + lunch_type:wkly_study_hours + 
    parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours, data = df_4_mdl_write)

plot(step_as_lm_write)

plot(stepwise_model_math)
## Warning: not plotting observations with leverage one:
##   190

step_as_lm_math=lm(formula = math_score ~ gender + ethnic_group + parent_educ + 
    lunch_type + test_prep + parent_marital_status + practice_sport + 
    is_first_child + transport_means + wkly_study_hours + ethnic_group:transport_means + 
    parent_educ:parent_marital_status + parent_educ:is_first_child + 
    lunch_type:practice_sport + lunch_type:transport_means + 
    test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child + 
    parent_marital_status:transport_means + parent_marital_status:wkly_study_hours + 
    is_first_child:transport_means + is_first_child:wkly_study_hours,data = df_4_mdl_math)
plot(stepwise_model_read)